Level 1 Advanced Mathematics
Trig Test Review
Name:
May 11, 2012
NO-CALCULATOR SECTION
1.
Label the approximate location of the angle on the unit circle and then fill in the
missing information in the table.
Angle
Degrees
Angle
Radians
w/π
5p
2
Cosine of
Angle
Sine of
Angle
-135º
p
330º
2p
3
2. Evaluate using special triangles or the unit circle.
a. csc
2p
3
e. sin360°
b. tan
c. sec
p
4
f. csc240°
3p
4
g. sec90°
5p
d. cot
6
h. tan180°
3. Write the equation for a sinusoid that is described below:
A sinusoid with an amplitude of 5 units, a period of 16 minutes, a phase shift to
the left by 7 for a sine wave, and a vertical shift up 3 units.
___________________________________________
4. Solve each problem for x in the given interval.
a.
cot x = 3, 0 £ x £ p
b.
1 3p
sin x = - ,
£ x £ 2p
2 2
5. Use the function given below to answer each question.
æ æ p öö
y = 5 cosç 4ç x + ÷÷ - 2
è è 4 øø
a. What is the period of the graph?
________________________
b. What is the phase shift of the graph?
________________________
c. What is the amplitude of the graph?
________________________
d. What is the domain of the graph?
________________________
e. What is the range of the graph?
________________________
f.
Identify the graph below that represents the function given above. Circle the correct
graph.(Note: Graphs range from - 2p £ x £ 2p , - 10 y £ 10 , and has an x-scale by
p
4
and a y-
scale by 1.)
i.
ii.
iii.
iv.
6. Evaluate: a) cos-1(sin 5/6)
b) sin-1(tan 7/4)
2
CALCULATOR SECTION
7.
Graph at least one cycle of
f ( x ) = -1+ 5 sin
all critical values for one complete cycle.
p
( x + 2).
6
State the period, and label
8. Given that a = 10, and c = 26, find all remaining sides and angles. In other words, solve the
right triangle, DABC .
A
c
b
C
a
B
9. From a distance of 20 ft away from the base, the angle of elevation to the top of a tree is 45.
How tall is the tree?
3
10. Point P(-5,9) is on the terminal side of angle . Evaluate the six trigonometric functions for
.
a. sin  = _______________
d. csc  = _______________
b. cos  = _______________
e. sec  = _______________
c. tan  = _______________
f. cot  = _______________
11. Use the given triangle to evaluate the six trigonometric functions for .
g. sin  = _______________
h. cos  = _______________
i. tan  = _______________
j. csc  = _______________
20
k. sec  = _______________
l. cot  = _______________

21
12. Find the length of the arc intercepted by a central angle of
radius of 2.
2p
radians in a circle with a
3
13. You are standing at a point on the north rim of the Grand Canyon, 7256 ft above sea level.
When you look across to the south rim, the angle of depression from your line of sight to the
south rim is 19. The south rim is 6159 ft above sea level. How wide is the canyon at that point?
14. Princess Rapunzel is standing on the top of her 125 ft tower, gazing down at her Prince
Charming as he walks towards her. At first glance, the angle of depression from Rapunzel to
Prince Charming is 20. At second glace, the angle of depression is 35. How far has the Prince
traveled in the time between Rapunzel’s first and second glance?
4
15. Buried Treasure Problem
You seek a treasure that is buried in the side of a mountain. The
mountain range has a sinusoidal cross section. The valley to the left
is filled with water to a depth of 50 m, and the top of the range is
150 m above the water level. You set up an x-axis at water level
and a y-axis 200 m to the right of the deepest part of the water. The
top of the mountain is at x = 400m.
a) Write the equation expressing y in terms of x for points on the surface of the mountain.
b) Show by calculation that this sinusoid contains the origin (0, 0)
c) The treasure is located within the mountain at the point (x, y) = (130, 140).(Note this point is
not on the graph). Which would be a shorter way to dig to the treasure, a horizontal tunnel or a
vertical tunnel? Justify your answer.
16. Extraterrestrial Being Problem
5
Researchers find a creature from an Alien Planet. Its body temperature is varying sinusoidally
with time. Thirty five (35) minutes after they start timing, it reaches a high of 120F. Twenty
(20) minutes after that it reaches its next low of 104 F.
a. Sketch the graph of this sinusoid.
b. Write the equation of the sinusoid.
c. What is the temperature when they first start timing?
d. Find the first two times that the extraterrestrials temperature is 114F.
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