Math 154 Trigonometry Sample Exam #4 Name: __________________
Sample Trigonometry chapter 6 and 7 exam.
Show all work and draw a picture when appropriate. Each question is worth 10pts.
1. Use exact values to solve for x if 0 ≤ x < 2π:
0csccotsin2 =−+ xxx
2. Use exact values to solve for x if 0 ≤ x < 360º:
sin cos 1
3. Find all exact solutions for
θ
: 2sin32cos
=
θ
+
θ
4. Find all degree solutions to the following:
(
)
2
3
453sin −=°−x
5. The two equal sides of an isosceles triangle are each 38 centimeters. If the base
measures 48 centimeters, find the measure of the two equal angles.
6. Solve for B if A = 40°, b = 62 m and a = 54 m.
7. Solve for B if A = 30°, b = 40 m and a = 10 m.
8. A man wandering in the desert walks 3.3 miles in the direction of S 44o W. He then
turns and walks 2.2 miles in the direction of N 55o W. At that time, how far is he
from his starting point, and what is his bearing from his starting point?
9. Given the two vectors
2, 3 and
3, 6, find the angle between them.
10. Given any real numbers a and b, prove that
, and
, are
perpendicular.