# Trigonometric Identities

Trigonometric Identities. x and y are independent variables, ; e is the base of the natural logarithm. The following indefinite integrals involve all of these well-known trigonometric functions. Improve your math knowledge with free questions in "Trigonometric identities I" and thousands of other math skills. There are loads of trigonometric identities, but the following are the ones you're most likely to see and use. Below are some of the most important definitions, identities and formulas in trigonometry. The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. Pythagorean Identities. The Essential Trigonometric Identities. Trigonometric Formulas for Sum and Difference, Double Angle, Half Angle, Product and Periodicity Identities. ©2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 p <. Loading Close. 2 Proving a Trigonometric Identity Deﬁnition 14. The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. But it can, at least, be enjoyable. ; d is the differential operator,. Plan your 60-minute lesson in Math or Precalculus and Calculus with helpful tips from Tiffany Dawdy. Based on the success we had in using power series to define the complex exponential (see Section 5. Motivation: Trig Is Anatomy. We dare you to prove us wrong. Trigonometric Identities. The Trigonometric Identities are equations that are true for Right Angled Triangles. Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the side of the right triangle. Trig identities are the combination of one or more trigonometric functions. Various identities and properties essential in trigonometry. Quotient Identities. Trying to keep up with trig can be hard at first -- suddenly you're learning new terms like sine, cosine, and tangent, and having to figure out more triangles than you ever cared about. How to use Trigonometric Identities to Simplify Expressions using examples and step by step solutions, Algebraic Manipulation of Trigonometric Functions, Distributive Property, FOIL, Factoring, Simplifying Complex Fractions, Multiplying, Dividing, Adding and Subtracting Fractions, Multiplying, Dividing, Simplifying. These functions aren't available in earlier versions. We will also cover evaluation of trig functions as well as the unit circle (one of the most important ideas from a trig class!) and how it can be used to evaluate trig functions. Double Angle Formulae. Below is a list of what I would consider the essential identities. To do so, you will need to use your algebraic background to show that the expression on one side of the equals sign can be changed into the expression on the other side of the equals sign. Students' understanding of trigonometric functions discussion of procepts primarily occurred within the context of elementary arithmetic, Gray and Tall stressed that their construct can be applied to. pdf - Free download as PDF File (. Integration using trig identities or a trig substitution mc-TY-intusingtrig-2009-1 Some integrals involving trigonometric functions can be evaluated by using the trigonometric. How to use Trigonometric Identities to Simplify Expressions using examples and step by step solutions, Algebraic Manipulation of Trigonometric Functions, Distributive Property, FOIL, Factoring, Simplifying Complex Fractions, Multiplying, Dividing, Adding and Subtracting Fractions, Multiplying, Dividing, Simplifying. College Trigonometry Version bˇc Corrected Edition by Carl Stitz, Ph. Superposition Relationships. It contains basic trig identities and formulas. Includes full solutions and score reporting. Learn and use Trigonometric Identities: Quotient Identities, Reciprocal Identities, Pythagorean Identities, Cofunction Identities, Sum Identities, Difference Identities, Double Angle Identities, Even-Odd Identities Sum to Product Identities, Product to Sum Identities, Half-Angle Identities. Trigonometry plays a major role in musical theory and production. 2 Proving a Trigonometric Identity Deﬁnition 14. Basic Definitions. List of trigonometric identities 3 Related identities Dividing the Pythagorean identity through by either cos2 θ or sin2 θ yields two other identities: Using these identities together with the ratio identities, it is possible to express any trigonometric function in terms of. Reciprocal identities. txt) or read online for free. An Engineers Quick Trigonometry Laws and Identities Reference. An identity is a mathematical statement that equates one quantity with another. The main trigonometric functions are sine, cosine, and tangent, often written as sin(x), cos(x), and tan(x). There are loads of trigonometric identities, but the following are the ones you're most likely to see and use. Trigonometric Functions of Acute Angles. Learn basic trig formulas and simple steps to solve trig identities. Pythagorean Identities. Yes, Trigonometric Identities isn't particularly exciting. Free trigonometric identities - list trigonometric identities by request step-by-step. tan 2 θ + 1 = sec 2. Complex numbers Up: math_prelims Previous: Vectors and vector algebra Trigonometric identities. Integration using trig identities or a trig substitution mc-TY-intusingtrig-2009-1 Some integrals involving trigonometric functions can be evaluated by using the trigonometric. Trigonometric Identities. Trigonometry. This is an arbitrary measurement, and we may choose other ways to divide a circle. Superposition Relationships. , y = 12" - Sin Y 7. An example of a trigonometric identity is sin ⁡ 2 θ + cos ⁡ 2 θ = 1. An identity is a mathematical statement that equates one quantity with another. Free Precalculus worksheets created with Infinite Precalculus. Architecture: Trigonometric identities are found heavily in architecture. These trigonometry identities are true for all values of the variables. tan 2 θ + 1 = sec 2. Je Zeager, Ph. Below we make a list of derivatives for these functions. The fundamental formulas of angle addition in trigonometry are given by. And you use trig identities as constants throughout an equation to help you solve problems. Pythagorean Trigonometric Identity (1) Trig ID Movie (II) Trig ID Movie (III) Even/Odd Identities. The Six Basic Trigonometric Functions. Trigonometric Identities. The main goal in dealing with trigonometric expressions is to simplify them. The following problems require the use of these six basic trigonometry derivatives :. The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. Integration using trig identities or a trig substitution mc-TY-intusingtrig-2009-1 Some integrals involving trigonometric functions can be evaluated by using the trigonometric. Recall the definitions of the reciprocal trigonometric functions, csc θ, sec θ and cot θ from the trigonometric functions chapter:. Starting from the Pythagorean Theorem and similar triangles, we can find connections between sin, cos, tan and friends (read the article on trig). There is no set method that can be applied to verifying identities; there are, however, a few different ways to start based on the identity which is to be verified. Let's quickly recap the major steps and ideas that we discovered in our previous lesson. For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). (If it is not a Right Angled Triangle go to the Triangle Identities page. Fundamental trigonometric identities. Based on the success we had in using power series to define the complex exponential (see Section 5. The cofunction identities show the relationship between sine, cosine, tangent, cotangent, secant and cosecant. Now that we have become comfortable with the steps for verifying trigonometric identities it’s time to start Proving Trig Identities!. ©2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 p <. Hence, sin + sin = 2sin + 2. Type your expression into the box to the right. We use MathJax. The always-true, never-changing trig identities are grouped by subject in the following lists. Simple Functions; Logarithm and Exponential Functions; Hyperbolic and Inverse Hyperbolic Functions. Quotient Identities. MCR3U Trigonometric identities worksheet Prove the following trigonometric identities by showing that the left side is equal to the right side. In mathematics, the trigonometric functions are a set of functions which relate angles to the sides of a right triangle. These are called Pythagorean identities because they're just the good old Theorem of Pythagoras in new clothes. Free Precalculus worksheets created with Infinite Precalculus. We will also cover evaluation of trig functions as well as the unit circle (one of the most important ideas from a trig class!) and how it can be used to evaluate trig functions. The following identities, involving two variables, are called trigonometric addition identities. Trigonometric functions allow us to use angle measures, in radians or degrees, to find the coordinates of a point on any circle—not only on a unit circle—or to find an angle given a point on a circle. Trigonometry is the branch of mathematics that deals with the study of: angles triangles (tri means three, tri-angles means $3$ angles) lateral and angular relationships of planar and three-dimensional figures. Trig identities are notoriously difficult to memorize: here's how to learn them without losing your mind. Sound waves travel in a repeating wave pattern, which can be represented graphically by sine and cosine functions. Calculus Definitions >. The following problems require the use of these six basic trigonometry derivatives :. The main goal in dealing with trigonometric expressions is to simplify them. In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x). Summary of trigonometric identities You have seen quite a few trigonometric identities in the past few pages. Then everything involving trig functions can be transformed into something involving the exponential function. In order to prove trigonometric identities, we generally use other known identities such as Pythagorean identities. Alternative pdf link. When solving, simplify with the identities initially, if you can. Trigonometric functions are used to describe properties of any angle, relationships in any triangle, and the graphs of any recurring cycle. The Trigonometric Identities are equations that are true for Right Angled Triangles. , y = 12" - Sin Y 7. Mathematics is definitely among the top fears of students across the globe. Identities involving trig functions are listed below. cot 2 (x) + 1 = csc 2 (x). Summary : Calculator wich uses trigonometric formula to simplify trigonometric expression. Use these fundemental formulas of trigonometry to help solve problems by re-writing expressions in another equivalent form. Three of them involve only squares of functions. Based on the success we had in using power series to define the complex exponential (see Section 5. TOP Interview Coding Problems/Challenges Run-length encoding (find/print frequency of letters in a string) Sort an array of 0's, 1's and 2's in linear time complexity. Costenoble This Section: 4. Sine function (EMA53) Functions of the form $$y=\sin\theta$$ (EMA54) Worked example 16: Plotting a sine graph. Type your expression into the box to the right. Lakeland Community College Lorain County Community College. Choose from 500 different sets of trig identities flashcards on Quizlet. In this section we will give a quick review of trig functions. Summary : Calculator wich uses trigonometric formula to simplify trigonometric expression. pdf - Free download as PDF File (. We use MathJax. The Pythagorean Identities - Cool Math has free online cool math lessons, cool math games and fun math activities. Trigonometry is an entire semester-long class (sometimes two!), so it isn't possible to put all of the identities here. Trigonometric Addition Formulas. Trigonometric identities allow us to simplify a given expression so that it contains sine and cosine ratios only. Trigonometric Identities. The basic inverse trigonometric identities come in several varieties. The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. Password *. Here are some examples of simple identity proofs with reciprocal and quotient identities. Simple Functions; Logarithm and Exponential Functions; Hyperbolic and Inverse Hyperbolic Functions. However, there are often angles that are not typically memorized. Learn how to solve trigonometric equations and how to use trigonometric identities to solve various problems. Can we go deeper? Maybe we can connect sine. The Six Basic Trigonometric Functions. In algebraic form, an identity in x is satisfied by some particular value of x. Sound waves travel in a repeating wave pattern, which can be represented graphically by sine and cosine functions. A complete list of trig identities grouped by type. 5-2 Verifying Trigonometric Identities. Trigonometry plays a major role in musical theory and production. Here are the formulas for these six trig ratios: Given a triangle, you should be able to identify all 6 ratios for all the angles (except the right angle. Previous concepts explained how to use trigonometry to find the measures of the angles and sides of right triangles. Trigonometric identity is an equality which remains true for entire values of the variables involved in the equation. sin(x y) = sin x cos y cos x sin y. Trigonometric identities are simply ways of writing one function using others. Mathematics is definitely among the top fears of students across the globe. Problems on Trigonometric Identities with Solutions - Concept - Problems with step by step explanation. Motivation: Trig Is Anatomy. Trigonometric Identities S. Connect with social media. Trigonometry practice problems Try solving these as much as you can on your own, and if you need help, look at the hidden solutions. Loading Close. He considered every triangle—planar or spherical—as being inscribed in a circle, so that each side becomes a chord (that is, a straight line that connects two points on a curve or surface, as shown by the inscribed triangle ABC in. A Trigonometry equation is an expression that may hold true or false for any angle. In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. 2 - Trigonometric identities We begin this section by stating about 20 basic trigonometric identites. Learn trig identities with free interactive flashcards. The basic inverse trigonometric identities come in several varieties. Students' understanding of trigonometric functions discussion of procepts primarily occurred within the context of elementary arithmetic, Gray and Tall stressed that their construct can be applied to. Free practice questions for Trigonometry - Trigonometric Identities. Typically, to do these proofs, you must always start with one side (either side, but usually take the more complicated side) and manipulate the side until you end up with the other side. Various identities essential in hyperbolic trigonometry. Trig Identities. pdf - Free download as PDF File (. The common thing for them is that they express the ratios between different sides of a right-angled triangle, from the point of view of the angle of interest, and thus some of them are transformations of the others. 2 Trigonometric identities (EMBHH). Students use TI-Nspire calculators to develop their own understandings of what trigonometric identities are and why they work. Trigonometric Identities are some formulas that involve Trigonometric functions. The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. Linking to this page. The following problems require the use of these six basic trigonometry derivatives :. Let's quickly recap the major steps and ideas that we discovered in our previous lesson. Trigonometry and Complex Exponentials Amazingly, trig functions can also be expressed back in terms of the complex exponential. \sin^2 \theta + \cos^2 \theta = 1. The Elementary Identities Let (x;y) be the point on the unit circle centered at (0;0) that determines the angletrad: Recall that the de nitions of the trigonometric functions for this angle are. List of trigonometric identities 3 Related identities Dividing the Pythagorean identity through by either cos2 θ or sin2 θ yields two other identities: Using these identities together with the ratio identities, it is possible to express any trigonometric function in terms of. The Essential Trigonometric Identities. To enter a value, click inside one of the text boxes. Lecture Notes Trigonometric Identities 1 page 3 Sample Problems - Solutions 1. It is satisfied for all values of x. This video is unavailable. Trigonometric functions are functions of an angle. This is a great tool in which students and teachers can use all through out Trigonometry. The six basic trigonometric functions can be defined using a right triangle: The six trig functions are sine, cosine, tangent, cosecant, secant, and cotangent. Be prepared to need to think in order to solve these equations. The fundamental (basic) identities discussed in the previous section involved only one variable. txt) or read online for free. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant, cosine, cotangent, secant, sine, and tangent. Trig_calculator online. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics. If you would like to make links to this page, you can customize the link so it points to a particular identity or group of identities. 2 Proving a Trigonometric Identity Deﬁnition 14. Page was constructed with the help of Suzanne Cada. There are many trigonometric functions, the 3 most common being sine, cosine, tangent, followed by cotangent, secant and cosecant. Trigonometry is the branch of mathematics that deals with the study of: angles triangles (tri means three, tri-angles means $3$ angles) lateral and angular relationships of planar and three-dimensional figures. Starting from the Pythagorean Theorem and similar triangles, we can find connections between sin, cos, tan and friends (read the article on trig). This is an arbitrary measurement, and we may choose other ways to divide a circle. From a general summary to chapter summaries to explanations of famous quotes, the SparkNotes Trigonometric Identities Study Guide has everything you need to ace quizzes, tests, and essays. Below we make a list of derivatives for these functions. Choose from 500 different sets of trig identities flashcards on Quizlet. 2 Trigonometric identities (EMBHH). Identities involving trig functions are listed below. DO NOT BLINDLY APPLY powers and roots across expressions that have or signs. Summary of trigonometric identities You have seen quite a few trigonometric identities in the past few pages. Ellermeyer An identity is an equation containing one or more variables that is true for all values of the variables for which both sides of the equation are de-ned. Summary : Calculator wich uses trigonometric formula to simplify trigonometric expression. However, there are often angles that are not typically memorized. 1), we have reason to believe this approach will be fruitful for other elementary functions as well. \sin^2 \theta + \cos^2 \theta = 1. Sine function (EMA53) Functions of the form $$y=\sin\theta$$ (EMA54) Worked example 16: Plotting a sine graph. The main trigonometric functions are sine, cosine, and tangent, often written as sin(x), cos(x), and tan(x). The identities in the attached image can be used to determine that other trigonometric equations are also identities. The six basic trigonometric functions can be defined using a right triangle: The six trig functions are sine, cosine, tangent, cosecant, secant, and cotangent. ; d is the differential operator,. The unit circle is an excellent guide for memorizing common trigonometric values. Can we go deeper? Maybe we can connect sine. Based on the success we had in using power series to define the complex exponential (see Section 5. Without new words, humans are hard to describe: "There's a sphere at the top, which gets scratched occasionally" or "Two elongated cylinders appear to provide locomotion". sin 2 (x) + cos 2 (x) = 1. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics. Some of the f. The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. Trigonometric identities are simply ways of writing one function using others. pdf - Free download as PDF File (. Trigonometric Identities (Revision : 1. Trigonometric Formulas for Sum and Difference, Double Angle, Half Angle, Product and Periodicity Identities. arcsinh(z) = ln( z + (z 2 + 1) ). Trigonometric Identities and Formulas. Trigonometric functions are elementary functions, the argument of which is an angle. TRIGONOMETRY FORMULAS cos 2 (x) +sin 2 (x) =1 1+ tan 2 (x) = sec 2 (x) cot 2 (x) +1= csc 2 (x) cos( ) cos( )cos( ) sin( )sin( ) sin( ) sin( )cos( ) cos( )sin( ) x y x. Motivation: Trig Is Anatomy. Trigonometric Identities are some formulas that involve Trigonometric functions. The always-true, never-changing trig identities are grouped by subject in the following lists. Recall that dividing a circle into 360 parts creates the degree measurement. These trigonometry identities are true for all values of the variables. A complete list of trig identities grouped by type. x and y are independent variables, ; e is the base of the natural logarithm. In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined. This page will try to simplify a trigonometric expression. Derivation of Trigonometric Identities, page 3 Since uand vare arbitrary labels, then and will do just as well. Description : This calculator allows through various trigonometric formula to calculate trigonometric expression. ; d is the differential operator,. Simple Functions; Logarithm and Exponential Functions; Hyperbolic and Inverse Hyperbolic Functions. Ask your doubt of trigonometric identities and get answer from subject experts and students on TopperLearning. The following problems require the use of these six basic trigonometry derivatives :. Problems on Trigonometric Identities with Solutions - Concept - Problems with step by step explanation. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. org Math Tables: Hyperbolic Trigonometric Identities Hyperbolic Definitions sinh(x Inverse Hyperbolic Defintions. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant, cosine, cotangent, secant, sine, and tangent. The following are the basic trigonometric identities and are true for all angels except those for which either side of the equation is undefined:. Recall from geometry that a complement is defined as two angles whose sum is 90. Trigonometry questions, for grade 12 , related to identities, trigonometric equations, are presented along with their solutions and detailed explanations. Recall the definitions of the trigonometric functions. Sine function (EMA53) Functions of the form $$y=\sin\theta$$ (EMA54) Worked example 16: Plotting a sine graph. Download as PDF file. Without new words, humans are hard to describe: "There's a sphere at the top, which gets scratched occasionally" or "Two elongated cylinders appear to provide locomotion". The significance of an identity is that, in calculation, we may replace either member with the other. USEFUL TRIGONOMETRIC IDENTITIES De nitions tanx= sinx cosx secx= 1 cosx cosecx= 1 sinx cotx= 1 tanx Fundamental trig identity (cosx)2 +(sinx)2 = 1 1+(tanx)2 = (secx)2 (cotx)2 +1 = (cosecx)2. The basic inverse trigonometric identities come in several varieties. Analytic Trigonometry, which includes double angle formulas, trig ratios of the sum of 2 angles, trigonometric equations and inverse trig equations. Practice evaluating and proving expressions using the fundamental trigonometric formulas with these worksheets. Sum-Difference Formulas. These functions aren't available in earlier versions. Trigonometry is an entire semester-long class (sometimes two!), so it isn't possible to put all of the identities here. Summary •This outlines the basic procedure for solving and computing inverse trig functions •Remember a triangle can also be drawn to help with the. sec8sin8 tan8+ cot8 sin' 8 5. Fortunately, you do not have to remember absolutely every identity from Trig class. Trigonometric Ratio is known for the relationship between the measurement of the angles and the length of the side of the right triangle. Identities involving trig functions are listed below. pdf - Free download as PDF File (. It is convenient to have a summary of them for reference. Learn basic trig formulas and simple steps to solve trig identities. , sin, cos, tan, etc. ) Each side of a right triangle has a name: Adjacent is always next to the angle. Fundamental trigonometric identities. Basic Inverse Trig Function Identities. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Trigonometric functions describe the relation between the sides and angles of a right triangle. 6 An identity is an equation that is true for every possible value of the variable. Learn trig identities with free interactive flashcards. sin 2 θ + cos 2 θ = 1. Improve your math knowledge with free questions in "Trigonometric identities I" and thousands of other math skills. Pre-Calc Trigonometric Identities The six trigonometric functions/The six trigonometric functions Trig Identities Cheat Sheet. Integration using trig identities or a trig substitution mc-TY-intusingtrig-2009-1 Some integrals involving trigonometric functions can be evaluated by using the trigonometric. This is an arbitrary measurement, and we may choose other ways to divide a circle. But it can, at least, be enjoyable. For example, from the table above we see that This equivalence is called an identity. Imagine Bob The Alien visits Earth to study our species. Typically, to do these proofs, you must always start with one side (either side, but usually take the more complicated side) and manipulate the side until you end up with the other side. Trigonometric functions allow us to use angle measures, in radians or degrees, to find the coordinates of a point on any circle—not only on a unit circle—or to find an angle given a point on a circle. Integrals of Trigonometric Functions. A comprehensive list of the important trigonometric identity formulas. Compound Angle Formulae. Law of Sines Law of Cosines Law of Tangents Mollweid's Formula. Trigonometry. Now that we have become comfortable with the steps for verifying trigonometric identities it's time to start Proving Trig Identities!. Free math lessons and math homework help from basic math to algebra, geometry and beyond. Complex Trigonometric and Hyperbolic Functions. Introduction. Basic Definitions. If it holds true then it is a Trigonometry identity otherwise they are termed as conditional equations. When we integrate to get Inverse Trigonometric Functions back, we have use tricks to get the functions to look like one of the inverse trig forms and then usually use U-Substitution Integration to perform the integral. This article contains a trig functions list that should help you do well in trigonometry. Includes full solutions and score reporting. Sine and Cosecant Functions (Special Property) Sine Identity; Cosine and Secant Functions (Special Property) Cosine Identity; Tangent and Cotangent Functions (Special Property) Tangent Identity; Cofunction Identities. You're going to need to be familiar with trigonometric identities (or at least know where to look for them). cos(x y) = cos x cosy sin x sin y. secx - tanx SInX - - ­ secx 3. Trigonometry practice problems Try solving these as much as you can on your own, and if you need help, look at the hidden solutions. 2 Trigonometric identities (EMBHH). Trigonometric identities are used to manipulate the trigonometric equations of some specific forms. Once you have reviewed the identities thoroughly, you may take the quiz below. On this page we will present the main identities. This is a great tool in which students and teachers can use all through out Trigonometry. cos ' Y -sin. TRIGONOMETRY FORMULAS cos 2 (x) +sin 2 (x) =1 1+ tan 2 (x) = sec 2 (x) cot 2 (x) +1= csc 2 (x) cos( ) cos( )cos( ) sin( )sin( ) sin( ) sin( )cos( ) cos( )sin( ) x y x. Let's quickly recap the major steps and ideas that we discovered in our previous lesson. These trigonometry identities are true for all values of the variables. Complex Trigonometric and Hyperbolic Functions. Which group of. An identity is a mathematical statement that equates one quantity with another. Trigonometric Identities and Formulas. Although the educational system presents numerous opportunities for students to enjoy developing new skills, excelling at sports, and practicing public speaking, it seems that nothing is working when it comes to mathematics. Trigonometric Identities are some formulas that involve Trigonometric functions. Trigonometric Identities. 2 - Trigonometric identities We begin this section by stating about 20 basic trigonometric identites. Get the free "Trigonometric Identities" widget for your website, blog, Wordpress, Blogger, or iGoogle. Solving Triangles Using The Law of Sines. Trig Laws Math Help. For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). USEFUL TRIGONOMETRIC IDENTITIES De nitions tanx= sinx cosx secx= 1 cosx cosecx= 1 sinx cotx= 1 tanx Fundamental trig identity (cosx)2 +(sinx)2 = 1 1+(tanx)2 = (secx)2 (cotx)2 +1 = (cosecx)2. Below are some of the most important definitions, identities and formulas in trigonometry.