pre cal worksheet

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Math 1083 Worksheet 8 Getting Ready for Trigonometric Equations with Identities

Objectives: 1. Review notation for powers of trigonometric functions

2. Apply trigonometric identities

(1) Notation review

Recall: sinn 𝑥 = (sin 𝑥)𝑛

#1. Evaluate each expression

a) cos2 ( 𝜋

6 ) b) sin3 (

𝜋

6 )

#2. Factor each

a) sin2 𝑥 − cos2 𝑥 b) tan3 𝑥 + tan 𝑥 sec 𝑥

(2) Trigonometric identities

Pythagorean Identities cos2(𝑡) + sin2(𝑡) = 1

1 + tan2(𝑡) = sec2(𝑡)

1 + cot2(𝑡) = csc2(𝑡)

Reciprocal Identities

csc(𝑡) = 1

sin(𝑡)

sec(𝑡) = 1

cos(𝑡)

cot(𝑡) = 1

tan(𝑡)

Even/odd properties sin(−𝑡) = − sin(𝑡) csc(−𝑡) = − csc(𝑡)

cos(−𝑡) = cos(𝑡) sec(−𝑡) = sec(𝑡)

tan(−𝑡) = − tan(𝑡) cot(−𝑡) = − cot(𝑡)

#3 Write each in terms of sin 𝑥

a) cos2 𝑥 b) 3 sin2 𝑥 − 4 cos2 𝑥

#4 Write each in terms of sec 𝑥

a) tan2 𝑥 b) tan 𝑥

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#5. Write the expressions in terms of sine and cosine and then simplify each of the following to an

expression involving a single trigonometric function.

a) sec 𝑡

csc 𝑡 b)

cot 𝑡

csc 𝑡

c) 1+tan 𝑥

1+ cot 𝑥 d)

cos(−𝜃)

cot(𝜃)

e) 𝑐 sc 𝑡 – sin 𝑡

cos 𝑡 f)

cot 𝑥

csc 𝑥−sin 𝑥

g) −𝑡𝑎𝑛(−𝑥)𝑐𝑜𝑡(−𝑥) h) sin 𝑥 cos 𝑥 sec 𝑥