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

Warm Up 14.3  Identify the trig function equivalent to the given function. 2

14.3 Verify Trigonometric Identities  Objective:  Verify trigonometric identities. 3

Reciprocal Identities  sin θ = csc θ =  cos θ =sec θ =  tan θ =cot θ = 4

Trig Identities  An identity is an equation that is true for all real values in the domain of the variable. 5

Quotient Identities  tan θ =  cot θ = 6

Pythagorean Identities  sin 2 θ + cos 2 θ =  1 + tan 2 θ =  1 + cot 2 θ = 7

Cofunction Identities 8

Negative Angle Identities Or, “Even/Odd Identities”  sin (–θ) =  cos (–θ) =  tan (–θ) = 9

Example 1  Given that and, find the values of the other 5 trig functions. 10

Checkpoints 1 & 2  Find the values of the other five trig functions. 11

Example 2  Simplify the expression. 12

Checkpoint 3  Simplify the expression. 13

Example 3  Verify the identity. 14

Checkpoint 4  Verify the identity. 15

Homework 14.3  Practice