Name:________________
Block:___________
2017 Pre-Calculus Quarter 3 Test Review
Analytic Trigonometry (Chapter 6)
Find values to answer the following questions.
3

1. If tan    when     and
4
2
5
3
when
cos  
   2 , what is the exact
13
2
value of tan(    ) ?
3. If cos  
value of sin
3
3
   2 , what is the
and
5
2

2
2. When P(2, -5) is on the terminal side of θ in
standard position, what is the value of
cos 2θ?
4. What is the solution of sin θ = 0.8704 to the
nearest hundredth of a degree? 0 < θ < 360o
?
5. What is the solution of sec θ = 1.8492 to the
nearest hundredth of a radian? 0 < θ < 2π.
6. What are the solution(s) of
2 cos 2   1  3 cos  if θ is in the interval
[0, 2π)?
Solve the equations below on the interval 0 < θ < 2π.
7. cos2 θ – 1 = 0
8. 2 sin   3  4
Applications of Trigonometry (Chapter 7)
Solve each triangle.
9.
B
19
10. α = 115°, β = 25°, a = 180
a
32
A
11. β = 50°, a = 20, b = 30
b
C
12. a = 14, b = 9, c = 21
13. Give the general solution for the equation.
3 tan 2 x −1 = 0
15. For θ in the interval [0, 2π), what are the
solutions of the equation below?
2sin(3θ ) + 1 = 0
14. Solve the equation for θ ∈ [0, 2π).
2 cos x + 2sin 2x = 0
16. Observers at points A and B are directly in
line with a hot-air balloon and are themselves 115
feet apart. The angle of elevation from
observer A to the balloon is 75°, and
the angle of elevation from observer
B to the balloon is 50°. How high
is the hot-air balloon?
50°
115 ft
75°
Exponential & Logarithmic Functions (Chapter 4)
17. Solve
42 x  7  64 x 5
19. Solve
e3 x  2  12
18. Solve
x5  x7
20. True or False?
(Please write a word for your answer.)
a) log8 24 – log8 3 = 1
b)
1
log 4  log 3 4
3
c)
log 6 7  log
7
6
d) log7 12 + log7 5 = log7 17
21. What is the sum of the solutions of
log (15x – 36) = 2 log x?
The sum of the solutions is
.
22. Solve.
23. Solve.
log2 x  13  5
log3 ( x  9)  log9 x  0
24. Solve
10e3 x 7  5
25. Solve
log 1
4
26. A cup of coffee, having a temperature of
180°F, is taken out of the microwave and placed
in a room which is 70°F. After 4 minutes, the
temperature of the coffee is 160°F. How long
from the time the coffee is taken out of the
microwave will it be until the temperature of the
coffee is 130°F?
(16) 2
x
22
27. The half-life of plutonium-241 is 13 years. If
1000 grams are present now, how much will be
present in 30 years?
1
28. Graph. y = ( ) x1  1
2
Domain:______________ Range:_____________Asymptote:_________
Increasing/Decreasing Function:__________________
29. Graph. y = 41 x  2
Domain:______________ Range:_____________Asymptote:_________
Increasing/Decreasing Function:__________________
30. Graph.
y  1  log 2 (2  x)
Domain:_____________Range:_____________Asymptote:_________
Increasing/Decreasing Function:__________________
31. Graph. y = 2log3 x  2
Domain:______________ Range:_____________Asymptote:_________
Increasing/Decreasing Function:__________________