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Exam 4, Math 100, PreCalculus, Fall 2016, DeBonis (50 points)
[1.] (12 points) Answer the following trigonometric questions:
a. Convert
π
9
to degrees.
b. Compute sec 7π
.
6
c. Given csc θ < 0 and sec θ = 3, find the value of tan θ.
[2.] (9 points) Find all solutions to the following equation for 0 ≤ x < 2π (answers should
be exact and in radians):
2 sin2 x +
√
3 sin x = 0
[3.] (10 points) Graph one cycle of the following trigonometric function:
π
f (x) = −2 cos 2πx +
+1
2
[4.] (6 points) Verify the following trigonometric identity:
(sin x + cos x)(tan x + cot x) = sec x + csc x
[5.] (5 points) Rewrite the following without trigonometric functions:
tan sec−1
√ x
[6.] (8 points) Two poles of height 100 feet and 80 feet are attached by a wire (see diagram
below)
a. Find the exact value of d if θ = 60◦ .
b. Find the value of θ to the nearest degree if d = 40 feet.
[7.] (8 points) (Extra Credit) Estimate to the nearest degree the value of θ in the
diagram below: