Name:
Math 1060
Exam 3 Review
1. Graph the following functions:
(a) 2 sin(πx + π) − 1
(c) 2 sec4 (5x) − 4
(b) tan(3x) − 1
2. Suppose sin u = 35 , sin v = 12 , cos u > 0, cos v < 0. Compute the following:
(p) cot u + π2
(q) sec u + π3
(a) cos u
(e) cot u
(i) csc v
(m) cot(u − v)
(b) tan u
(f) cos v
(j) cot v
(n) sin(u + π)
(c) sec u
(g) tan v
(k) sin(u + v)
(o) cos(u − pi)
(d) csc u
(h) sec v
(l) tan(u − v)
3. Simplify:
(a)
1−sin2 x
csc2 x−1
π
2
− φ cos φ
(b) sin y sec y + cos y csc y
(c) cot
(b) csc α − sin α = cos α cot α
(c) sin4 x − sin2 x = cos4 x − cos2 x
(b) 2 sin2 x + sin x − 1 = 0
(c) sin x − cos x = 1
4. Verify:
(a) sin2 θ − cos2 θ = 2 sin2 θ − 1
5. Solve:
(a) 2 sin ξ + 1 = 0
6. Using fundamental trigonometric identities (those from §5.1) and sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
show that cos(a − b) = cos(a) cos(b) + sin(a) sin(b).
7. Your brother drags your sled up a hill with a 15◦ incline. If he dragged you 100 feet, how much elevation did you gain?
8. You are standing 50 feet from your brother’s model rocket launchpad. The rocket launches vertically.
If θ is the angle of elevation from you to the rocket, and s is the distance from you to the rocket, write
θ as a function of s.
9. You tie your brother to the ceiling of the living room using a bungee cord. He starts out 6 feet from
the ground, falls down to 2 feet from the ground, then bounces up and down indefinitely in simple
harmonic motion (meaning it can be described in terms of sin or cos). If it takes him 43 seconds each
bounce to fall from 6 feet to 2 feet:
(a) Find the amplitude and period of your brother’s motion.
(b) Write down his height h as a function of seconds passed t.
(c) When is he 3 feet off the ground?
(d) Graph at least one full period of your brother’s height function.