MATH 130 EXAM
MATH 130 (Precalculus) Spring 2020
Exam 3
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: 11 − 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