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Name___________________________ Exam Date ________________ ANSWERS POSTED ON WIKI
UNIT #2 TRIGONOMETRY ~ REVIEW PRECALCULUS 20
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. What is the reference angle for 15in standard position?
A 255
C 345
B 30
D 15
____
2. What are the three other angles in standard position that have a reference angle of 54?
A 99144234
C 144234324
B 108162216
D 126234306
____
3. What is the exact cosine of A?
A
18
B
18
C 18
D
A
B 1
____
4. The point (40, –9) is on the terminal arm of A. Which is the set of exact primary trigonometric ratios for the
angle?
A
,
,
B
C
D
____
,
,
,
,
,
,
5. Marco is 450 m due east of the centre of the park. His friend Ray is 450 m due south of the centre of the park.
Which is the correct expression for the exact distance between the two boys?
A
C
m
m
B
D
m
m
1
____
6. An angle is in standard position such that
. What are the possible values of , to the nearest degree,
if
?
A 6 and 174
B 6 and 276
____
C 84 and 264
D 84 and 276
7. Which of the following triangles cannot be solved using the sine law?
Diagrams not drawn to scale.
A
C
22
68º
76º
43º
21
B
24
D
11
20
32º
13
43º
Completion
Complete each statement.
1. The expression cos 30° is equivalent to sin ____________________.
2. The tangent ratio is positive in the first and ____________________ quadrants.
Matching Match the correct term to its description below.
A reference angle
D ambiguous case
B cosine law
E sine law
C angle in standard position
F terminal arm
____ 1. a problem with two or more solutions
:
____
2. a law used when two sides and an opposite angle are given
____
3. the acute angle between the terminal arm and the x-axis of an angle in standard position
____
4. an angle with the initial arm on the positive x-axis
____
5. a law used when two sides and a contained angle are given
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Short Answer
1. The hypotenuse of a right isosceles triangle is 5 cm long.
a) Write an exact expression for the base and the height of the right triangle, using primary trigonometric
ratios.
b) Use your expressions to determine the exact area of the triangle.
2. The point A(–3, –5) is on the terminal arm of an angle . Determine exact expressions for the primary
trigonometric ratios for the angle.
3. Diana is designing a triangular race course for a sailing regatta. The course is triangular and has a 35° angle
between two sides of 7 km and 6 km. What is the length of the third side of the race course, to the nearest
kilometre?
4. a) For the given trigonometric ratio, determine two other angles that give the same value.
i) sin 45°
ii) tan 300°
iii) cos 120°
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Problem
1. The point (–5, 7) is located on the terminal arm of A in standard position.
a) Determine the primary trigonometric ratios for A.
b) Determine the primary trigonometric ratios for an B that has the same sine as A, but different signs for
the other two primary trigonometric ratios.
c) Use a calculator to determine the measures of A and B, to the nearest degree.
2. Consider A such that cos A =
.
a) In which quadrant(s) is this angle? Explain.
b) If the sine of the angle is negative, in which quadrant is the angle? Explain.
c) Sketch a diagram to represent the angle in standard position, given that the condition in part b) is true.
d) Find the coordinates of a point on the terminal arm of the angle.
e) Write exact expressions for the other two primary trigonometric ratios for the angle.
3. Two wires are connected to a tower at the same point on the tower. Wire 1 makes an angle of 45° with the
ground and wire 2 makes an angle of 60° with the ground.
a) Represent this situation with a diagram.
b) Which wire is longer? Explain.
c) If the point where the two wires connect to the tower is 35 m above the ground, determine exact
expressions for the lengths of the two wires.
d) Determine the length of each wire, to the nearest tenth of a metre.
e) How do your answers to parts b) and d) compare?
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4. Gursant and Leo are both standing on the north side of a monument that is 6.0 m tall. Leo is standing 3.5 m
closer to the monument than Gursant. Leo measures the angle from the ground to the top of the monument to
be 41°. Determine the angle that Gursant would measure from the ground to the top of the monument, to the
nearest degree.
5. In
, c = 11 cm, b = 7 cm, and
.
a) Sketch possible diagrams for this situation.
b) Determine the measure of C in each diagram.
c) Find the measure of A in each diagram.
d) Calculate the length of BC in each diagram.
6. One of the tallest totem poles in the world is located in Alert Bay, British Columbia. When the angle of
elevation of the sun is 62°, the totem pole casts a shadow that is 30 m in length. Suppose the totem pole is
vertical. How tall is the totem pole, to the nearest tenth of a metre?
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7. Jason is standing 8.7 km from town X and 11.5 km from town Y. From where he stands, the angle between
the two towns is 37°. A new hotel has just been built on the road connecting town X and town Y, exactly
halfway between the two towns. From where Jason is standing, he sees that the angle of elevation to the top of
the hotel is 1°. Determine the height of the hotel, to the nearest tenth of a metre. Include a diagram with your
solution.
8. A racing bicycle has spokes on each wheel that are 35 cm long. Each spoke forms a 30° angle with the
adjacent spoke. What is the distance between the points where the spokes attach to the wheel, rounded to the
nearest centimetre?
9. Chang is participating in a charity bicycle road race. The route starts at Centreville and travels east for 13 km
to Eastdale. He then makes a 135° turn and heads northwest for another 18 km, arriving at Northcote. The
final leg of the race returns to Centreville.
a) What is the total length of the race, to the nearest tenth of a kilometer?
b) What are the angles in the triangle formed by the three towns, to the nearest degree?
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