Properties: Trigonometric Identities

Slides:

Advertisements

Similar presentations

The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.

Advertisements

An identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established and establish.

The Trigonometric Functions What about angles greater than 90°? 180°? The trigonometric functions are defined in terms of a point on a terminal side r.

11. Basic Trigonometric Identities. An identity is an equation that is true for all defined values of a variable. We are going to use the identities to.

Ch 7 – Trigonometric Identities and Equations 7.1 – Basic Trig Identities.

10.3 Verify Trigonometric Identities

EXAMPLE 1 Find trigonometric values Given that sin  = and <  < π, find the values of the other five trigonometric functions of . 4 5 π 2.

What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.

Trigonometric Identities

Aim: Co-functions & Quotient Identities Course: Alg. 2 & Trig. Aim: What are the Co-functions and Quotient Identities in Trigonometry? Do Now: =

12-2 Trigonometric Functions of Acute Angles

Right Triangle Trigonometry

6.2.2 The Trigonometric Functions. The Functions Squared sin 2 (  ) = sin(  ) 2 = sin(  ) * sin(  ) sin 2 (  ≠ sin (  2 ) = sin (  *  )

Basic Trigonometric Identities In this powerpoint, we will use trig identities to verify and prove equations.

Example 1 Verify a Trigonometric Identity The left-hand side of this identity is more complicated, so transform that expression into the one on the right.

13.1 Trigonometric Identities

Trigonometric Identities An identity in math is : - an unconditional statement of equality - true for all values of the variable(s) for which the equation.

EXAMPLE 1 Evaluate trigonometric functions given a point Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six.

Verify a trigonometric identity

Fundamental Trigonometric Identities Reciprocal Identities Tangent and Cotangent Identities Pythagorean Identities.

BELL-WORK TCAP Bell-Work # What is the cotangent of angle x if sec(x) = 12 5.

Trigonometry Section 8.4 Simplify trigonometric expressions Reciprocal Relationships sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Ratio Relationships.

Pythagorean Identities Unit 5F Day 2. Do Now Simplify the trigonometric expression: cot θ sin θ.

Copyright © Cengage Learning. All rights reserved. 5.2 Verifying Trigonometric Identities.

Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1.

Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established.

Section 8-4 Relationships Among the Functions. Recall…

Warm Up Answers Mastery Objectives 5.2 Verify trigonometric identities. Determine whether equations are identities.

Trigonometric Identities

Section 4.2 The Unit Circle.

Trigonometric Identities and Equations

Using Fundamental Identities

WARM UP 1. What is the exact value of cos 30°?

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

TRIGONOMETRIC IDENTITIES

Analytic Trigonometry

Fundamental Trigonometric Identities Essential Questions

Section 5.1 Trigonometric Identities

Section 5.1A Using Fundamental Identities

5 Trigonometric Identities.

Using Fundamental Identities

Basic Trigonometric Identities

Trigonometric Functions: The Unit Circle 4.2

Ch. 5 – Analytic Trigonometry

14.3 Trigonometric Identities

7.2 Verifying Trigonometric Identities

Section 5.1: Fundamental Identities

Lesson 6.5/9.1 Identities & Proofs

MATH 1330 Section 5.1.

Lesson 5.1 Using Fundamental Identities

17. Basic Trigonometric Identities

One way to use identities is to simplify expressions involving trigonometric functions. Often a good strategy for doing this is to write all trig functions.

7 Trigonometric Identities and Equations

Basic Identities Trigonometric Identities Section 3.1

Trigonometric Identities

Using Fundamental Identities

Using Fundamental Identities

Graphing Tangent and the Reciprocal Functions

Copyright © Cengage Learning. All rights reserved.

Multiple-Angle and Product-to-Sum Formulas (Section 5-5)

Math /4.4 – Graphs of the Secant, Cosecant, Tangent, and Cotangent Functions.

TRIGONOMETRIC IDENTITIES

WArmup Rewrite 240° in radians..

Day 60 Agenda Quiz # minutes

7.3 Sum and Difference Identities

Trigonometric Identities

Verifying Trigonometric

Presentation transcript:

Properties: Trigonometric Identities A trigonometric identity is a trigonometric equation that is true for all values except those for which the expressions on either side of the equal sign are undefined. Properties: Trigonometric Identities Reciprocal Identities Tangent & Cotangent Identities Pythagorean Identities

Ex 1: Verify the Pythagorean identity 1 + tan2 θ = sec2 θ

(sin x + cos x)2 = 1 + 2(sin x)(cosx) Ex 2: Verify the identity (sin x + cos x)2 = 1 + 2(sin x)(cosx)

Ex3: Simplify cscθtanθ

Attachments