Download Trig Exam 1 Review

LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
Trigonometry Exam 1 Review: Chapters 1, 2, 3
To adequately prepare for the exam, try to work these review problems using only the trigonometry knowledge which you
have internalized and the departmental formula sheet which is attached at the end of this review. No peeking at your notes,
homework, text, solutions manual, or other resources.
Note:
Anytime you are asked to perform a calculation manually or to give an exact answer, you may not use a calculator.
Chapter 1: Trigonometric Functions
1.
Find (a) the complement and (b) the supplement of 61°. Show all work and / or support your answer.
2.
Perform the calculation 84° 15' 39" – 23° 31' 51" manually. Show all work and / or support your answer.
3.
Manually convert 37° 11' 29" to decimal degrees. Round to the nearest thousandth of a degree. Show all work
and / or support your answer.
4.
Manually convert the angle 165.8525° to degrees, minutes, and seconds. Show all work and / or support your answer.
5.
Find the smallest positive coterminal angle for –1234°. Show all work and / or support your answer.
6.
Sketch the angle θ = 553° in standard position. What quadrant does it terminate in? Draw an arrow representing the
correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal
with θ. Show all work and / or support your answer.
7.
A tire is rotating 320 times per minute. Through how many degrees does it rotate in 8 seconds? Show all work
and / or support your answer.
8.
Find the exact values of the six trigonometric functions for the angle in standard position having the point
its terminal side. Rationalize denominators if applicable. Show all of your work.
9.
Suppose that the point (x, y) is in quadrant IV. Decide whether the ratio r is positive or negative. Show all work
and / or support your answer.
10.
Manually evaluate the expression cot 270 o − 3 sec180 o + 2 sin 2 90 o . Show all work and / or support your
answer.
11.
Use the appropriate reciprocal identity to find tan θ, if cot θ = −
( 3 , − 1) on
y
5
. Rationalize denominators when applicable.
3
Show all work and / or support your answer.
12.
Identify the quadrant or quadrants for the angle satisfying the condition cos θ < 0, csc θ > 0. Show all of your work.
13.
Give the signs of the sine, cosine, and tangent functions for 472°. Show all work and / or support your answer.
14.
Is the statement sin θ = 1.256 possible? Explain why it is or is not.
15.
Use identities to find sin θ, if sec θ = 2, with θ in quadrant IV. Show all work and / or support your answer.
16.
Find all trigonometric function values for the angle θ if tan θ =
and / or support your answer.
17.
Use the reciprocal, quotient, and Pythagorean identities to give three expressions that complete the following
3 in Quadrant III. Show all work
statement: cot θ = ________________________________________________________________________.
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LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
Chapter 2: Acute Angles and Right Triangles
18.
Match the trigonometric function in the first row with its value in the second row. Do not use a
calculator. Show all work and / or support your answer.
a.
csc 60°
3
A.
3
b. cos 45°
B.
2
2
C.
D.
2
3
c. tan 30°
2 3
E.
3
F.
1
2
19.
ABC is a right triangle with side lengths a = 3 and b = 5 and a 90° angle at C. Find the length
of side c and the six trigonometric function values for angle B. Do not use a calculator.
Show all work and / or support your answer.
20.
Write csc 25.4° in terms of its cofunction. Show all work and / or support your answer.
21.
Find one solution for the equation sin (2θ + 10°) = cos (3θ – 20°). Show all work and / or support your answer.
22.
Give the exact value of (a) sec 45° and (b) cot 30°. Show all work and / or support your answer.
23.
In the diagram below, find the exact value of each part labeled with a variable. Show all work and / or support your
answer.
24.
Match each angle in the first row with its reference angle in the second row. Show all work and / or support your
answer.
a.
284°
A. 30°
b.
–225°
c. 780°
B.
14°
C. 45°
D. 76°
E.
60°
F.
–45°
25.
Find exact values of the six trigonometric functions for: (a) 480° (b) –135° (c) 330°. Show all work and / or support
your answer.
26.
Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. Show all work and / or support
your answer.
a.
sec θ = − 2
b. tan θ =
3
27.
Use a calculator to find a decimal approximation for sec 147° 11'. Round your answer to four decimal places.
Show all work and / or support your answer.
28.
Find a value of θ in the interval [0°, 90°] for which cot θ = 1.2575516. Show all work and / or support your answer.
29.
Use a calculator to evaluate cos 100° cos 80° – sin 100° sin 80°. Show all work and / or support your answer.
30.
A car traveling on a 1.8° uphill grade has a grade resistance of 65.96 lb. What is the weight of the car? Show all work
and / or support your answer.
31.
Solve the right triangle shown below. Show all work and / or support your answer. Answers should be shown with
the correct number of significant digits.
2
LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
32.
Solve the right triangle ABC where a = 76.4 yd, b = 39.3 yd, and C = 90°. Give angles in degrees and minutes.
Show all work and / or support your answer. Answers should be shown with the correct number of significant digits.
33.
An airplane is flying at 30,250 ft above ground level. The angle of depression from the plane to the base of a tree is
17° 34'. How far must the plane travel horizontally to be directly over the tree? Show all work and / or support your
answer. Your answer should be shown with the correct number of significant digits.
34.
The angle of elevation from the top of a small building to the top of a nearby taller building is 46° 40', while the angle
of depression to the bottom is 14° 10'. If the smaller building is 28.0 m high, find the height of the taller building.
Show all work and / or support your answer. Your answer should be shown with the correct number of significant
digits.
35.
Two ships leave port at the same time. The first ship sails on a bearing of 40° at 18 knots (nautical miles per hour) and
the second at a bearing of 130° at 26 knots. How far apart are they after 1.5 hrs? Show all work and / or support your
answer. Your answer should be shown with the correct number of significant digits.
36.
The bearing from Elliston to Pangle is N 42° E. The bearing from Pangle to Themster is S 48° E. A car driven at
60 mph takes 1 hr to go from Elliston to Pangle and 1.8 hr to go from Pangle to Themster. Find the distance from
Elliston to Themster. Show all work and / or support your answer. Your answer should be shown with the correct
number of significant digits.
37.
An antenna is erected on the roof a building. From a point 182 feet in front of the building, the angle of elevation to
the base of the antenna is 67.3°, while the angle of elevation to the top of the antenna is 68.1°. Find the height of the
antenna. Show all work and / or support your answer. Your answer should be shown with the correct number of
significant digits.
Chapter 3: Radian Measure and Circular Functions
38.
Convert (a) 135°, (b) 345°, and (c) 240° 45' to radians. Show all work and / or support your answer. On parts a and b,
express your answer in terms of π. On part c, round your answer to three decimal places.
39.
Convert (a)
40.
⎛ 5π ⎞
Find the exact value of tan⎜ −
⎟ . Do not use a calculator. Show all work and / or support your answer.
⎝ 6 ⎠
7π
−4π
, (b)
, and (c) 8.9012 to degrees. Show all work and / or support your answer.
3
4
41.
Use the arc length formula to find the missing variable. Show all work and / or support your answer.
π
3π
a. θ = , r = 12, find s.
b. s = 6, r = 4, find θ.
c. θ =
, s = 6π, find r.
3
4
42.
Find the distance in kilometers between Halifax, Nova Scotia, 45° N, and Buenos Aires, Argentina, 34° S. Show all
work and / or support your answer. [Hint: The radius of the earth is about 6400 km.] Your answer should be shown
with the correct number of significant digits.
43.
Find the radius of a pulley if a rotation of 51.6° raises the weight 11.4 cm. Show all work and / or support your
answer. Your answer should be shown with the correct number of significant digits.
44.
A small gear and a large gear are meshed. An 80.0° rotation of the smaller gear causes the larger gear to rotate 50.0°.
Find the radius of the larger gear if the smaller gear has a radius of 11.7 cm. Show all work and / or support your
answer.
45.
Find the area of a sector of a circle having radius r = 90.0 km and central angle θ = 270°. Show all work and / or
support your answer.
3
LHS Trig 8th ed
46.
Trig Exam 1 Review F07 O’Brien
Find the exact values of (a) sin θ, (b) cos θ. and (c) tan θ for θ =
−3π
. Do not use a calculator. Show all work
2
and / or support your answer.
11π
17π
, (b) csc
. Show all work and / or support your answer.
6
4
47.
Find the exact circular function value for (a) tan
48.
Find a calculator approximation for cot (-8.3429). Show all work and / or support your answer.
49.
Find the value of t in the interval [0,
50.
Find the value of t in the given interval that has the given circular function value. Do not use a calculator. Show all
work and / or support your answer.
a.
51.
π
2
] such that csc t = 1.0219. Show all work and / or support your answer.
1
⎡π ⎤
⎢ 2 , π ⎥ ; cos t = − 2
⎦
⎣
b.
3
⎡ 3π ⎤
⎢ π, 2 ⎥ ; tan t = 3
⎦
⎣
c.
2
⎤
⎡ 3π
⎢ 2 , 2π ⎥ ; sin t = − 2
⎦
⎣
Suppose that point P is on a circle with radius 10 cm, and ray OP is rotating with angular speed
π
18
radians per second.
a.
Find the angle generated by P in 6 sec. Show all work and / or support your answer.
b.
Find the distance traveled by P along the circle in 6 sec. Show all work and / or support your answer.
c.
Find the linear speed of P. Show all work and / or support your answer.
2π
radians per sec and t = 3 sec , use the formula for angular speed to find θ. Show all work and / or
3
support your answer.
52.
Given ω =
53.
Given v = 9 m per sec and r = 5 m, use the formula for linear speed to find ω . Show all work and / or support your
answer.
54.
Given s =
216π
5
yd, r = 9 yd, and ω =
2π
5
radians per second, use the formulas for arc length and angular speed to
find t. Show all work and / or support your answer.
55.
The tires of a bicycle have radius 13 in. and are turning at the rate of 200 rpm. How fast is the
bicycle traveling in mph? Show all work and / or support your answer. [Hint: 5280 ft = 1 mile.]
4
LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
Answers
Chapter 1: Trigonometric Functions
1.
29°; 119°
10. 5
2.
60° 43' 48"
11. −
3.
37.191°
12. II
4.
165° 51' 9"
13. sin θ is positive; cos θ and tan θ are negative
5.
206°
6.
III; 193°; -167°
7.
15,360°
14. not possible
3
15. −
2
3
1
cos θ = −
tan θ = 3
16. sin θ = −
2
2
2 3
3
sec θ = -2 cot θ =
csc θ = −
3
3
8.
sin θ = −
1
cos θ =
2
csc θ = -2
9.
sec θ =
3
2
tan θ = −
2 3
3
3
3
17.
3 5
5
1
cos θ
;
; ±
tan θ sin θ
(csc θ − 1)
2
cot θ = − 3
y
will be negative because y is negative in Q IV and r is always positive.
r
Chapter 2: Acute Angles and Right Triangles
18.
E; B; A
26. 135°; 225°; 60°; 240°
19.
c=
27. -1.1899
34
sin B =
5 34
34
cos B =
3 34
34
csc B =
34
5
sec B =
34
3
tan B =
cot B =
5
3
28. 38.491580°
3
5
29. -1
20.
sec 64.6°
30. 2100 lbs
21.
θ= 20°
31. 38.8°; 154; 198
22.
2;
32. 85.9; 62° 50'; 27° 10'
3
23.
a = 12; b = d = 12 3 ; c = 12 6
33. 95,550 ft
24.
D; C; E
34. 146 m
25a.
sin 480° =
b.
3
1
cos 480° = −
tan 480° = − 3
2
2
2 3
3
sec 480° = -2 cot 480° = −
csc 480° =
3
3
sin (-135°) = −
35. 47 nautical miles
36. 120 miles
2
2
cos (-135°) = −
tan (-135°) = 1
2
2
37. 17.7 ft
csc (-135°) = − 2 sec (-135°) = − 2 cot (-135°) = 1
c.
sin 330° = −
csc 330° = -2
1
2
cos 330° =
sec 330° =
3
2
2 3
3
tan 330° = −
3
3
cot 330° = − 3
5
LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
Chapter 3: Radian Measure and Circular Functions
38.
3π 23π
;
; 4.202
4
12
47. 1; -2
39.
-240°; 315°; 510°
48. .532
40.
3
3
49. 1.3634
41.
4π; 1.5; 8
50.
2π 7π 7π
;
;
3
6
4
42.
8800 km
51.
3π
; 23.562 cm; 3.927 cm per sec
4
43.
12.7 cm
52. 2π
44.
18.7 cm
53.
45.
19085.2 km2
54. 12 sec
46.
1; 0; undefined
55. 15.5 mph
9
rad per sec
5
6
LHS Trig 8th ed
Trig Exam 1 Review F07 O’Brien
7