Download MATH 2412 TEST 1 ANSWER ALL QUESTIONS. TIME 1.5HRS

MATH 2412 TEST 1
ANSWER ALL QUESTIONS. TIME 1.5HRS.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression if θ = 45°. Do not use a calculator.
1)
A)
1) _________
B) 2
C) 8
D)
Use the given triangles to evaluate the expression. Rationalize all denominators.
2) csc 30°
2) _________
A) 2
C)
B)
D)
Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the
given angle. Give an exact answer with a rational denominator.
3)
9
8
Find cos θ.
3) _________
A) cos θ =
Graph the function.
4) y = 3 cos ( 4x - π)
B) cos θ =
C) cos θ =
D) cos θ =
4) _________
A)
B)
C)
D)
Using a calculator, solve the following problems. Round your answers to the nearest tenth.
5) A ship leaves port with a bearing of N 44° W. After traveling 15 miles, the ship then turns 90° and travels on a
bearing of S 27° W for 13 miles. At that time, what is the bearing of the ship from port? 5) _________
A) N 84.9° W B) N 67.9° W C) N
40.9° W D) N 3.1° W
Find the exact value of the expression, if possible. Do not use a calculator.
6)
A)
6) _________
B) -
C)
D) -
Use the given triangles to evaluate the expression. Rationalize all denominators.
7) cot 45°
7) _________
A)
C) 1
B)
D)
Solve the problem.
8) A building 160 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the
measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume
the person's eyes are level with the top of the building.) 8) _________
A) 58° B) 32°
C) 39° D) 51°
Convert the angle in radians to degrees. Round to two decimal places.
9)
radians 9) _________
A) 721° B) 720° C) 722° D) 719°
Find the reference angle for the given angle.
10) -53.2°
10) ________
A) 37.3° B) 53.2° C) 53.7° D) 36.8°
Find the exact value of the indicated trigonometric function of θ.
11) tan θ = -
A)
,
θ in quadrant II
B) -
C)
Find cos θ.
11) ________
D) -
Use a calculator to find the value of the trigonometric function to four decimal places.
12) sin 0.4
12) ________
A) 0.9211
B) 1.0000
C) 0.3894
D) 0.0070
Find the length of the arc on a circle of radius r intercepted by a central angle θ. Round answer to two decimal places.
13) r = 9 feet, θ = 75° 13) ________
A) 11.78 feet B) 10.6 feet
C) 12.96 feet D) 9.42 feet
Find the exact value of the expression if θ = 45°. Do not use a calculator.
14) 4 cos θ
14) ________
A) -4
B) 2
C) -2
D) 4
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
15) (-
,
) Find cos θ.
A)
B)
C) -
15) ________
D) -
Solve the problem.
16) The height of the water, H, in feet, at a boat dock t hours after 7 A.M is given by
measured in seconds. Find the period. 16) ________
A) 150 B)
, where t is time
C) 150π D)
Using a calculator, solve the following problems. Round your answers to the nearest tenth.
17) A ship is 31 miles west and 9 miles south of a harbor. What bearing should the captain set to sail directly to harbor?
17) ________
A) N 16.2° E
B) N
61.2° E C) N 73.8° E
D) N 163.8° E
Convert the angle in radians to degrees. Round to two decimal places.
18) -2.54 radians
18) ________
A) -145.53°
B) 0.05° C) -0.04°
D) -145.96°
Determine the phase shift of the function.
19) y = 5 cos ( x +
) 19) ________
A)
units to the right B) π units to the left
C)
units to the left
D) 5π units to the right
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
20) r = 6 inches, s = 30 inches 20) ________
A)
radians
B) 5 radians
C) -5 radians
D) 5∘
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
21) ( 12, 16) Find csc θ.
21) ________
A)
B)
C)
D)
The given angle is in standard position. Determine the quadrant in which the angle lies.
22) -342°
22) ________
A) Quadrant III B) Quadrant II C) Quadrant I D) Quadrant IV
Solve the problem.
23) A straight trail with a uniform inclination of 15° leads from a lodge at an elevation of 800 feet to a mountain lake at
an elevation of 8500 feet. What is the length of the trail (to the nearest foot)?
23) ________
A) 7972 feet
B) 32,842 feet
C) 8800 feet
D) 29,751 feet
Determine the amplitude or period as requested.
24) Amplitude of y = 5 sin 3x 24) ________
A)
B) 5
C)
D)
Use reference angles to find the exact value of the expression. Do not use a calculator.
25) csc 960°
25) ________
A) -
B) -
C) -
D) -
Find a cofunction with the same value as the given expression.
26) csc
26) ________
A) sec
B) csc
C) cot
D) csc
Find the reference angle for the given angle.
27) 5.9
A) -0.38 B) 0.38 C) 2.76 D) -2.76
27) ________
Determine the phase shift of the function.
28) y = -2 cos (x +
A) -2 units up
C)
B)
) 28) ________
units to the left
units to the right D) -2 units down
The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicated
trigonometric function at t.
29)
A)
Find tan t.
B)
C)
29) ________
D)
Solve the problem.
30) The current I, in amperes, flowing through a particular ac (alternating current) circuit at time t seconds is
I = 110 sin
What is the period of the current?
30) ________
A)
second D) 75π seconds
second B)
second C)
Find a positive angle less than 360° that is coterminal with the given angle.
31) -234°
31) ________
A) 234° B) 306° C) -54° D) 126°
Convert the angle in radians to degrees.
32)
32) ________
A) 810° B) 80π° C) 160° D) 405°
The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicated
trigonometric function at t.
33)
A)
Find sec t.
B)
C)
D)
33) ________
1) A
2) A
3) D
4) B
5) A
6) D
7) C
8) B
9) B
10) B
11) D
12) C
13) A
14) B
15) D
16) A
17) C
18) A
19) B
20) B
21) D
22) C
23) D
24) B
25) D
26) A
27) B
28) B
29) C
30) A
31) D
32) D
33) B