I want to get answers my my math 125 quiz.
Quiz 9 – Spring
2
0
1
3 Math 125 Precalculus Name
Question 1: Simply the the expressions. Your answer should involve only sin t, cos t, and tan t.
(2 pts) (a) (sec t cot t− csc t tan t) sin t cos t
(2 pts) (b)
1
2 csc t cos t− 3 cot t
Question 2: Prove the following identities algebraically.
(2 pts) (a) tan θ =
1 − cos 2θ
2 cos θ sin θ
(2 pts) (b) (sin2 2πt + cos2 2πt)3 = 1
(2 pts) (c) sin4 x− cos4 x = sin2 x− cos2 x (2 pts) (d)
1 + sin θ
cos θ
=
cos θ
1 − sin θ
1
Quiz 9 – Spring 2013 Math 125 Precalculus Name
Question 3: Suppose that sin θ = 3/5 and θ is in the second quadrant. Find sin(2θ), cos(2θ), and tan(2θ)
exactly. (4 pts)
Question 4: Suppose p(x) = (1/x) + 1 and q(x) = x− 2.
(2 pts) (a) Let r(x) = p(q(x)). Find a formula for r(x) and simplify it.
(2 pts) (b) Write formulas for s(x) and t(x) such that p(x) = s(t(x)) , where s(x) 6= x and t(x) 6= x. Verify
that p(x) = s(t(x)).
(2 pts) (c) Let a be different from 0 and −1. Find a simplified expression for p(p(a)).
Question 5: Find the inverses of the functions.
(2 pts) (a) g(x) =
x− 2
2x + 3
(2 pts) (b) s(x) =
3
2 + log x
2
