mathWHIZ

MATH 115 Quiz 4 Summer 2018

Find the acute angle θ, to the nearest hundredth of a degree, for the given function value.

1) sin θ = 0.6831

Use the appropriate identity to find the indicated function value. No decimal answers.

2) cos θ, if sec θ = -4

3) Find sin θ if cos θ = 2/3 and θ is in quadrant IV.

4) Find cot θ if tan θ = √6

2 and θ is in quadrant III.

Without using a calculator, give the exact trigonometric function values with rational denominators.

5) tan 120°

6) sin 315°

7) tan 5π/6

Solve the problem.

8) In one area, the lowest angle of elevation of the sun in winter is 27°. Find the minimum distance x that a plant needing

full sun can be placed from a fence that is 6 feet high. Round your answer to the tenths place.

9) What arc length corresponds to a radius of 9.5 cm and a central angle of 5𝜋

12 ? Round to the nearest hundredth of a cm

Simplify the expression completely.

10) 10𝑡𝑎𝑛3𝑥

𝑠𝑒𝑐𝑥 ÷

5𝑡𝑎𝑛𝑥

𝑠𝑒𝑐𝑥

11) 𝑐𝑜𝑠2𝑥−2 cos 𝑥−8

cos 𝑥−4

12) Find 𝑠𝑖𝑛−1( −1

2 ) exactly in degrees.

13) Find tan 2θ, cos 2θ, and sin θ/2 where cos θ = -3/5 and θ is in quadrant III.

Solve, finding all solutions in [0, 2π) or [0°, 360°).

14) 2 cos(𝑡) = 6 cos(𝑡) − √12

15) cos 2x – cos x – 2 = 0