Name: ___________________________
Period: ________ Date: _____________
PreCalculus – Unit 9 Day 4 – Using Trig. Identities
Write each expression in terms of sine and cosine, then simplify.
1. cosx tanx
2. cot x sinx
sec x
csc x
3. sec x cos x
4.
5. sin x cos x tan x
6. sec x tan x csc x
7. sin x cot x sec x
Simplify using Pythagorean Identities where applicable.
8.
10.
sin 2 θ  cos 2 θ  cot 2 θ
csc θ
1  cos θ1  cos θ
sin θ
9.
11.
sin θ cos θ

csc θ sec θ
sin θ  cos θ2  1
cos θ
Combine expressions by writing them as fractions and finding a common denominator
algebraically.
12. sinθtanθ + cosθ
13. secθcscθ – cotθ
Rewrite each expression as a product using a greatest common factor. Then simplify.
14. sin3θ + sinθcos2θ
15. cotθsec2θ – cotθ
Simplify the expressions used in each equation. Then solve on an interval of [0, 2π).
16. 2cotθsinθ = 1
17. cosθtanθcsc2θ = 2
18. cosθtan2θcscθ = 1
****BONUS***** Write each equation in terms of only one trigonometric function either by
replacing sin2θ with 1 – cos2θ, or by replacing cos2θ with 1 – sin2θ. Then use factoring to solve
the resulting equation on an interval of [0, 2π).
19. sin2θ – cosθ – 1 = 0
20. 2cos2θ + sinθ – 2 = 0