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Mathematics 142 seventh homework
due Tuesday, November 3, 2015
please show your work to get full credit for each problem
1–2. Show why each identity is true:
(1)
1 − tan2 θ
+ 2 sin2 θ = 1
1 + tan2 θ
(2)
sin θ + cos θ − cos3 θ
= tan θ+sin2 θ
cos θ
3. For the angle A = sin−1
√
1 − m2
• draw a diagram of this angle A in a triangle, labeling all the side lengths
• compute the value of cos A
(your answer will involve m)
4. Sketch the points (x, y) in the plane for which (sin πx) (sin πy) ≥ 0
5. Find the domain of the function f (x) =
√
−4 sin 32x
6. Find all solutions of the trigonometric equation 3 sin 220πx −
π
6
= −2
7. Find all solutions of the trigonometric equation 3 cos 2x − 4 sin 2x = 1