St G Study Guide Name ________________________ Trigonometry

Verifying Identities

→ Change everything to sine and cosine ▪ Combine fractions

→ Use Pythagorean ID

→ Factor (GCF)

→ Starting with the fraction… ▪ If (+) or (–) in numerator→Split up fractions ▪ If (+) or (–) in denominator→ Multiply by the conjugate (to create a pythag ID)

Verify each identity below.

17) 1

1−sin𝑥= sec2 𝑥 + tan 𝑥 sec 𝑥

18) −sec 𝑥 − tan2 𝑥 sec 𝑥 = −sec3 𝑥

19)

20) cos 𝑥 cot 𝑥 = sec 𝑥 cot 𝑥 − sin𝑥

21) 1+cos𝑦

sec𝑦= cos𝑦 + cot2 𝑦

22) sec2 𝑥 + tan2 𝑥 =1+sin2 𝑥

cos2 𝑥

23)

24) sin𝑥

1+cos𝑥=

1−cos𝑥

sin𝑥

25)

26)

27)

28)

29) Which line of reasoning is correct when verifying the identity shown below? sec x – sec x sin2 x = cos x ?

a.

b.

c.

d.

Evaluating Expressions Determine the exact value of each expression (meaning no decimals!).