Download Pre-Test 1 (Sections 1

Test 1A
Name __Answer Key___________
1) Convert the angle 19°23’41” to a decimal in degrees. Round your answer to two
decimal places. (3 points)
1
1
 41 
60
3600
 19  0.383333  .011388
1923' 41"  19  23 
 19.394721
 19.39
____ 19.39 ____
2) Convert 2π/3 in radians to degrees. (2 points)
2 180

 120
3 
___ 120 ______
3) Distance between Cities. Salt Lake City, Utah, is due north of Flagstaff, Arizona.
Find the distance between Salt Lake City ( 40°45’ north latitude) and Flagstaff (
35°16’ north latitude). Assume that the radius of the Earth is 3960 miles. Round to
nearest whole mile. (3 points)
  4045' 3516 '  529 '  5 
s  r  (3960)  5.483333 

180
29
 5.483333
60
 378.9807
___ 379 _miles__
4) Use a calculator to find the approximate value of sec π/8. Round to 4 decimal
places. (2 points)
__ 1.0824 ______
Math 142 Precalculus II
1
3
, use trigonometric identities to find the exact values (no
4
5) Given cos 64° =
decimals) of
(a) sin 26 ° __
3
4
4 3
13
2
______ (b) sec 64° __
____ (c) sin 64° __
____
3
16
(1 point)
(2 points)
(3 points)
cos 2 64  sin 2 64  1
2
sec 64 
1
1

cos 64
3
4
4
4 3


3
3
 3
2

  sin 64  1
 4 
2
 3
2
   sin 64  1
 16 
13
sin 2 64 
16
6) A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty,
which is 305 feet tall. If the angle of elevation is 20°, how far is the ship from the
base of the statue? Round your answer to the nearest foot. (3 points)
tan 20 
305
305
, x
 837.9806
x
tan 20
__ 838 ft . _______
7) Use the reference angle to find the exact value (no decimals) of each expression.
Do not use the calculator. (2 points each)
(a) cos 405° ___
Math 142 Precalculus II
2
1
__ (b) sin (-30°) __- ______
2
2
(c) sin (-5π) ___0____
2
8)
Find the exact value of the remaining trigonometric functions of θ. (7 points)
tan θ = 1/3, θ in third quadrant
1
10
3
cos  
10
3
cot  
1
sin  
a 2  b2  c2
12  32  c 2
c  10
sin θ = _ 
10
___
10
cos θ = __ 
3 10
_
10
cot θ = ___3______
sec θ = __ 
10
__
3
csc θ = __  10 ___
9)
What is the y-intercept of y = tan x? (2 points)
_____0_________
10) For what numbers x, 0 ≤ x ≤ 2π, does cos x = 0? (2 points)

_______
2
,
3
2
________________________
11) Determine the amplitude and period of each function without graphing. Show how
Math 142 Precalculus II
3
you determined the period.
2 
(a) y  4sin  x  (3 points)
3 

(b) y  5cos 
2

x  (3 points)

Amplitude: ___4_______
Amplitude: ___5_______
Period:
Period:
___3π_______
___4_______
2
3
2 2
  3
2 3
3 2
2 
 4
 2
2 
12) Write the equation of a cosine function that has the given characteristics.
(a) Amplitute: 2, Period: 3π
(3 points)
(3 points)
2 
x  ________
3 
___ y  2 cos 
A  2,
T

T

2
_____ y  3cos 

x  _____

A3
2

2
(b) Amplitute: 3, Period: 4
T

2 2

3 3
13) Find an equation for the graph. (3 points)
Math 142 Precalculus II

2

2
T

2 

4
2
___ y  3sin
 2 x  _
4
14) Graph each function. Be sure to label the 5 key points. Use the graph to determine
the domain and range of each function.
(a) y  3cos(2 x)  1 (8 points)
       3 
(0, 2),  ,1 ,  , 4  , 
,1 ,  , 2 
4
2
4

 
 

y
4
3
2
1
x
-π
-π/2
π/2
π
-1
-2
Domain: ____All Reals________
Math 142 Precalculus II
Range: ____[-2, 4]_____________
5
(b)

y  2sin 
4

x  (8 points)

 2, 2 ,  4,0 ,  6, 2 , 8,0
(0,0),
y
2
(2,2)
1
x
(0,0)
1
2
3
(4,0)
4
5
6
7
(8,0)
8
-1
-2
(6,-2)
Domain: ____ All Reals _______ Range: ______[-2, 2]_________________
Math 142 Precalculus II
6