Name: ________________________ Class: ___________________ Date: __________
ID: A
Unit 5 PreCalculus Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the terminal point P (x, y) on the unit circle determined by t = −
π
4
. Round the values to the nearest
hundredth.
a. (0.71, –0.71)
b. (–0.71, –0.71)
c. (0.83, –0.85)
d. (–0.71, 0.71)
____
2. Find the terminal point P (x, y) on the unit circle determined by t = −
5π
. Round each value to the nearest
6
hundredth.
a. (0.87, –0.50)
b. (–0.99, 0.64)
c. (–0.87, 0.50)
d. (–0.87, –0.50)
____
19π
. Round the coordinates of
6
the terminal point to the nearest hundredth, and express the reference number in terms of π
3. Find the terminal point P (x, y) and the reference number determined by t =
a.
b.
c.
d.
terminal point is (–0.87, –0.50), reference number is
π
6
5π
terminal point is (–0.87, –0.50), reference number is
6
terminal point is (0.87, –0.50), reference number is
terminal point is (–0.87, 0.50), reference number is
1
π
6
π
6
Name: ________________________
____
ID: A
4. Use the figure to find the terminal point determined by the real number t = –0.59.
Round the values to one decimal place.
a.
b.
c.
d.
____
5. Find the exact values of the trigonometric functions sec
a.
b.
c.
____
terminal point is (–0.6, 0.8)
terminal point is (–0.8, –0.6)
terminal point is (0.6, 0.8)
terminal point is (0.8, –0.6)
13
π=
3
13
sec π =
3
13
7
π and csc π .
3
3
3
7
π=
3
3
7
3, cot π = 2
3
sec
3, csc
sec
2 3
13
7
π = 2, csc π =
3
3
3
ˆ
ÁÊÁ 3
7 ˜˜˜˜
Á
6. The terminal point determined by t is ÁÁÁ ,
˜ . Find sin t, cos t, and tan t.
ÁÁ 4 4 ˜˜˜
Ë
¯
7
3
7
a. sint = , cost = , tant =
4
4
3
b.
sin t =
7
7
3
, cost = , tan t =
4
4
3
c.
sin t =
3
7
7
, cost = , tan t =
4
4
3
2
Name: ________________________
____
ID: A
7. Find the values of the trigonometric functions of t if sint = −
a.
sint = −
13
13
, cost =
, tant =
7
7
13
6 13
, cot t =
6
13
b.
sint = −
13
6
, cost = − , tant =
7
7
13
6 13
, cot t =
6
13
c.
sint = −
13
6 13
6
13
, cost = , tan t =
, cot t =
7
13
7
6
13
and sec t < 0.
7
Short Answer
1. Find the terminal point P(x,y) on the unit circle determined by the given value of t =
2. Find the approximate value of the given trigonometric function.
tan(−4.3)
(a) By using the figure. Please give the answer to one decimal place.
tan(−4.3) = __________
(b) By using a calculator in radians. Please give the answer to five decimal places.
tan(−4.3) = __________
3
5π
.
3
Name: ________________________
ID: A
3. As a wave passes by an offshore piling, the height of the water is modeled by the function
ÊÁ π ˆ˜
h(t) = 3cos ÁÁÁ t ˜˜˜˜
ÁË 16 ¯
where h(t) is the height in feet above mean sea level at time t seconds.
(a) Find the period of the wave.
period = __________ seconds
(b) Find the wave height, that is, the vertical distance between the trough and the crest of the wave.
wave height = __________ feet
4. The carrier wave for an FM radio signal is modeled by the function
Ê Ê
ˆ ˆ
y = a sin ÁÁÁ 2π ÁÁ 9.65 × 10 7 ˜˜ t ˜˜˜
Ë
¯ ¯
Ë
where t is measured in seconds.
(a) Find the period of the carrier wave. Round the expression that precedes the multiplication sign to two
decimal places.
__________×10 − s
(b) Find the frequency of the carrier wave. Round the expression that precedes the multiplication sign to two
decimal places.
__________×10 − Hz
ÊÁ
ÁÁ 4
5. Suppose that the terminal point determined by t is ÁÁÁ ,
ÁÁ 7
Ë
4
33
7
ˆ˜
˜˜
˜˜ . Find the terminal point determined by t + π .
˜˜
˜
¯
Name: ________________________
ID: A
6. When a car hits a certain bump on the road, a shock absorber on the car is compressed a distance of 6 in.,
then released.
The shock absorber vibrates in damped harmonic motion with a frequency of 2 cycles per second. The
damping constant for this particular shock absorber is 2.3.
Find an equation that describes the displacement of the shock absorber from its rest position as a function of
time. Take t = 0 to be the instant that the shock absorber is released.
7. Each time your heart beats, your blood pressure increases, then decreases as the heart rests between beats. A
certain person's blood pressure is modeled by the function
p(t) = 90 + 20sin(160π t)
where p(t) is the pressure in mmHg at time t, measured in minutes. Find the amplitude, period, and frequency
of p.
8. Find a function that models the simple harmonic motion having the given properties. Assume that the
displacement is at its maximum at time t = 0.
amplitude 28 cm, period 8 s
9. Find the period and graph the function.
y = −7sec x
10. Find the period and graph the function.
y=
1
csc x
5
11. Sketch the graph.
1
y = 15sin x
2
5
Name: ________________________
ID: A
12. The point P is on the unit circle. The x-coordinate of P is
1
and P is in quadrant I. Find the point P(x, y).
7
7
1
13. Find the exact values of the trigonometric functions sin π and sin π .
6
6
14. Find the exact values of the trigonometric functions sec 9π and csc
6
1
π.
2
ID: A
Unit 5 PreCalculus Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
D
A
D
C
B
B
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
SHORT ANSWER
1. ANS:
ˆ
ÁÊÁ 1
3 ˜˜˜˜
ÁÁ
ÁÁ ,−
˜
ÁÁ 2
2 ˜˜˜
Ë
¯
PTS: 1
2. ANS:
–2.3; –2.28585
PTS: 1
3. ANS:
32; 6
PTS: 1
4. ANS:
1.04, -8; 9.65, 7
PTS: 1
5. ANS:
ÊÁ
ˆ
33 ˜˜˜˜
ÁÁÁ 4
ÁÁ − ,−
˜
ÁÁ 7
7 ˜˜˜
Ë
¯
PTS: 1
6. ANS:
f(t) = 6e −2.3t cos 4π t
PTS: 1
1
ID: A
7. ANS:
Amplitude 20, period 0.0125, frequency 80
PTS: 1
8. ANS:
f (t) = 28cos
π
4
t
PTS: 1
9. ANS:
period 2π
PTS: 1
10. ANS:
period 2π
PTS: 1
2
ID: A
11. ANS:
PTS: 1
12. ANS:
ÊÁ
ˆ˜
ÁÁ 1
˜
ÁÁ , 48 ˜˜˜
ÁÁ 7
7 ˜˜˜
Á
Ë
¯
PTS: 1
13. ANS:
7
1
sin π = −0.5, sin π = 0.5
6
6
PTS: 1
14. ANS:
sec 9π = −1, csc
1
π=1
2
PTS: 1
3