MATH 115 Quiz

1.Find the acute angle θ, to the nearest hundredth of a degree, for the given function value.
a. sin θ = 0.6131
Use the appropriate identity to find the indicated function value. No decimal answers.
b) cos θ, if sec θ = -4
c) Find sin θ if cos θ = 2/3 and θ is in quadrant IV.
d) Find cot θ if tan θ =√7
and θ is in quadrant III.
Without using a calculator, give the exact trigonometric function values with rational denominators.
i) tan 60°
ii) sin 135°
iii) tan 5π/6
Solve the problem.
2) In one area, the lowest angle of elevation of the sun in winter is 27.3°. Find the minimum distance x that a plant
needing full sun can be placed from a fence that is 5.7 feet high. Round your answer to the tenths place.
a) What arc length corresponds to a radius of 9.5 cm and a central angle of 5�
? Round to the nearest hundredth of a cm
Simplify the expression completely.
���2� ÷
c) ���2�−2 cos �−8
cos �−4
d)Find the amplitude, period or phase shift.
i) Find the amplitude of y = 5 cos (x – π).
ii) Find the period of y = 2 cos (2x + π/3).
iii) Find the phase shift of y = -4 + 3sin (5x – π/6)
iv) Find ���−1(−1
) exactly in degrees.
e) 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°).
i) 2 cos(�) = 6 cos(�) − √12
ii) cos 2x – cos x – 2 = 0