Download Pre-Test 1 (Sections 1

Pre-Test 1 (Sections 7.1 – 7.4, 7.6 – 7.7)
MATH 142
Section 7.1
1) Convert the angle 61°42’21” to a decimal in degrees. Round your answer to two
decimal places.
2) Convert the angle 61.24° to D°M’S” form. Round your answer to the nearest
second.
3) Convert 5π/6 in radians to degrees.
4) s denotes the length of the arc of a circle of radius r subtended by the central angle
θ. Find the missing quantity. Round your answer to three decimal places.
θ = ¼ radians,
s = 6 centimeters,
r=?
5) Distance between Cities. Charleston, West Virginia, is due north of Jacksonville,
Florida. Find the distance between Charleston ( 38°21’ north latitude) and
Jacksonville ( 30°20’ north latitude). Assume that the radius of the Earth is 3960
miles. Round your answer to the nearest mile.
Section 7.2
6) Use the definition or identities to find the exact value of each of the remaining five
trigonometric functions of the acute angle θ where tan θ =1/2.
7) Given cos 30° =
(a) sin 60 °
3
, use trigonometric identities to find the exact values of
2
(b) sec π/6
(c) sin 2 30°
Section 7.3
8) Find the exact value of the expression, 1 + tan2 30° - csc2 45°. Do not use a
calculator.
9) Use a calculator to find the approximate value of sec π/12. Round to 4 decimal
places.
10) Finding the Distance of a boat from shore. A person in a small boat, offshore
from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the
cliff. If the angle of elevation is found to be 30°, how far offshore is the ship? Round
to the nearest foot.
11) Finding the Distance between Two Objects. A blimp flying at an altitude of 500
feet, lies directly over a line from Soldier Field to the Adler Planetarium on Lake
1
Michigan. If the angle of depression from the blimp to the stadium is 32° and from
the blimp to the planetarium is 23°, find the distance between Soldier Field and the
Adler Planetarium. Round to the nearest foot.
Section 7.4
12) Name the quadrant in which the angle θ lies.
sin θ < 0, cos θ > 0
13) Find the reference angle of (a) 5π/6
(b) 7π/4.
14) Use the reference angle to find the exact value of each expression. Do not use the
calculator.
(a) cos 210°
(b) cos (-45°)
(d) cos (5π) .
(c) cos (-2π)
15) Find the exact value of the remaining trigonometric functions of θ.
cos θ = 3/5, θ in quadrant IV
Section 7.6
16) What is the y-intercept of y = cos x?
17) For what numbers x, -π ≤ x ≤ π, is the graph of y = cos x decreasing?
18) For what numbers x, 0 ≤ x ≤ 2π, does cos x = 0?
19) For what numbers x, -2π ≤ x ≤ 2π, does cos x = 1? Where does cos x = -1 ?
20) Determine the amplitude and period of each function without graphing.
(a) y  3cos(3x)
9
 3
(b) y  cos  
5
 2

x

21) Graph each function. Be sure to label the 5 key points. Verify the graph using a
graphing calculator. Use the graph to determine the domain and range of each
function.
(a) y  3sin x
1 
(b) y  2 cos  x 
4 
3

(c) y   cos 
2
4
 1
x
 2
22) Write the equation of a sine function that has the given characteristics.
(a) Amplitute: 2, Period: 4π
(b) Amplitute: 4, Period: 1
2
23) Find an equation for each graph.
(a)
y
9
8
7
6
5
4
3
2
1
x
-4π
-2π
2π
4π
6π
8π
10π
-1
-2
-3
-4
-5
-6
-7
-8
-9
(b)
3
y
2.5
2
1.5
1
0.5
x
-1
-0.5
0.5
1
1.5
2
2.5
-0.5
-1
-1.5
-2
-2.5
-3
Section 7.7
24) What is the y-intercept of y = cot x ?
25) For what numbers x, -2π ≤ x ≤ 2π, does csc x = 1 ? For what numbers x does csc
csc = -1 ?
3
26) Use a graphing calculator to graph one cycle of each function. Label 3 points for
the tan and cot functions and 2 points for the csc function. Use the graph to
determine the domain and range of each function.
1 
(a) y  tan  x 
2 

(b) y  cot 
4

x

1
(c) y  csc  2 x 
2
4