1. Answer the following questions:
a. Explain how we know that cos2θ+sin2θ=1.
b. Use the previous fact to prove 1+tan2θ=sec2θ
2. Verify the following identities:
a. 1+cot22θ=−sec2θ 1−csc θ
b. cosx =1+sinx 1−sinx cosx
3. Given sinθ= with
a. sin2θ
b. cos2θ
c. tan⎛⎜θ⎞⎟
⎝2⎠
. Evaluate the following.
4. Find the exact values of each of the following.
a. tan(22.5o)=
b. sin⎛⎜5π⎞⎟=
⎝12 ⎠
c. cos(87o)cos(93o)−sin(87o)sin(93o)
5. Solve the following trigonometric equation. Express solutions for 0≤θ<2π.
a. sinθcosθ=
b.
6. Verify the following identities.
a. cos⎛⎜π+θ⎞⎟=−sinθ
⎝ 2 ⎠
b. csc⎛⎜3π−θ⎞⎟=−secθ
⎝ 2 ⎠