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

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Presentation transcript:

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

Verifying Trigonometric Identities We are transforming one side of an equation to look like the other side using trigonometric identities and algebra. Either side may be transformed into the other side or both sides may be transformed into a simpler “3rd” form. Objective: 7-2 Verifying Trigonometric Identities

Example Verify that sec2x – tan x cot x = tan2x is an identity. Objective: 7-2 Verifying Trigonometric Identities

Steps 1. Transform the more complicated side of the equation to look like the simpler side. 2. Substitute one or more trigonometric identities to simplify expressions. 3. Factor or multiply to simplify expressions. 4. Multiply expression by an expression equal to 1. 5. Express all trigonometric functions in terms of sine and cosine. Objective: 7-2 Verifying Trigonometric Identities

Another Example Verify that is an identity. Objective: 7-2 Verifying Trigonometric Identities

Homework Problem #13 #15 Objective: 7-2 Verifying Trigonometric Identities

Simplifying Both Sides Verify that is an identity. Objective: 7-2 Verifying Trigonometric Identities

Another Example Verify that (sec x – tan x)(1 + sin x) = cos x Objective: 7-2 Verifying Trigonometric Identities

More Homework #19. Objective: 7-2 Verifying Trigonometric Identities

Simplifying Trig Equations - Example Find a numerical value of one trig function of x if Objective: 7-2 Verifying Trigonometric Identities

You Try Find a numerical value of one trig function of x if Objective: 7-2 Verifying Trigonometric Identities

Homework page 434, 13-16 all, 17, 19, 25, 29, 31 and 33 (challenge) Objective: 7-2 Verifying Trigonometric Identities