MATH 130 EXAM

MATH 130 (Precalculus) Spring 2020

Exam 3 Thursday, May 7

1. You are allowed to use the following resources: textbooks, notes, and lectures.

2. All other resources are prohibited. In particular, you may not discuss any aspect of the problems with other people, and you may not use other computational resources.

3. Write your answers on a separate piece of paper, and show all your work. Answers without appropriate work shown might not receive full credit.

4. Submit your exam via e-mail (NOT Gradescope) by 11:59PM on Friday, May 8.

5. In case I have any doubts that the work you submit is your own, I reserve the right to ask you to demonstrate your knowledge in a one-on-one video interview.

By signing your name below, you affirm that you understand the instructions and that you have neither given nor received unauthorized help on this exam.

I pledge that I have neither given nor received assistance on this exam.

Name (Print) Signature

Problem Value Points 1 15 2 15 3 15 4 15 5 15 6 10 7 15

Total 100

(1) Find real numbers a and d such that the graph of y = a cos x + d has y−intercept equal to (0, 3) and passes through the point ( 2π

3 , 0).

(2) Find real numbers b and c such that the graph of y = tan(bx + c) has x = π/4 as a vertical asymptote and has y−intercept equal to (0,−

√ 3).

(3) Find all solutions (in radians) of the equation

cos

( x +

π

2

) = sin x− 1.

(4) Find the exact value of cot(arcsin(−5 9 )). Your answer must be exact and in simplified form for full

credit.

(5) Verify the following identity: 1

1 − sin x −

1

1 + sin x = 2 sec x tan x

(6) If csc θ = 4 and cos θ < 0, find all six trigonometric functions of θ. Your answers must be exact and in simplified form for full credit.

(7) Find all solutions in the interval [0, 2π) of the equation

2 cos2 x− 3 cos x + 1 = 0

2