Trigonometry Review

Math 20-1
Name: _________________________________
Trigonometry Review
1. Sketch an angle in standard position with each given measure.
a) 24°
b) 104°
2. State the reference angle for each angle in standard position.
a) 55°
b) 155°
c) 255°
d)
355°
3. Determine the measure of the three other angles in standard position, 0° <  < 360°, that
have a reference angle of
a) 40°
b) 72°
4. Determine if the pair of angles has the same reference angle.
a) 50°, 140°
b) 200°, 290°
5. Use trigonometric ratios to determine the exact value of the length of side DE.
6. Sketch the angles in standard position so that the terminal arm passes through each point.
Write the sine, cosine, and tangent ratios for each angle as an exact value.
a) (1, 5)
b) (4, –3)
Math 20-1
Name: _________________________________
7. Determine the exact values of the sine, cosine, and tangent ratios for the angle in standard
postition.
8. Without using a calculator, state whether each ratio is positive or negative. Explain your
reasoning.
a) sin 100°
b) cos 200°
c) tan 300°
d)
sin 350°
9. An angle is in standard position with its terminal arm in the stated quadrant. Determine the
exact values for the other two primary trigonometric ratios for each.
a) sin θ =
–3
; quadrant III
5
b)
tan θ =
b)
tan θ =
–5
; quadrant II
12
10. Solve each equation for 0° ≤ θ < 360°.
a) sin θ =
c) cos θ =
–1
2
3
2
1
3
Math 20-1
11. Solve each equation, for 0° ≤ θ < 360°.
a) sin θ = 0.7760
Name: _________________________________
b)
cos θ = – 0.8090
c) tan θ = – 0.9004
12. Sketch each triangle. Then, determine the unknown side and angles. Identify the ambiguous
case and determine all solutions.
a) In ABC, AB = 15 m, BC = 5 m, and A = 20°.
b) In PQR, PQ = 12.5 cm, QR = 13.0 cm, and P = 103°.
13. A golf green is 6 m wide. Within what angle must a player hit the ball in order to land on the
green from a position about 20 m from the green?
Math 20-1
Name: _________________________________
14. Two planes left an airport and are flying in different directions. The angle between their
flight path is 47°. One hour later, plane A has travelled 850 km and plane B has travelled
900 km. How far apart are the two planes at this time? Round the distance to the nearest
kilometer.
15. Devin wants to approximate the height of the tree outside his house. From the ground, he
measures the angle of elevation to the top of the tree to be 65 degrees. He paces 3 m farther
away from the tree and measures the angle of elevation to be 55 degrees. Determine the
height of the tree to the nearest hundredth of a metre.
16. Given triangle ABC, ∠A = 30° and b = 42 cm. Determine the range of values for the length of
side a that could create each situation.
a) no triangle
b) one right triangle
c) two oblique triangles
Math 20-1
Name: _________________________________
KEY
1. a)
b)
2. a) 55˚
b) 25˚
c) 75˚
d) 5˚
3. a) 140˚, 220˚, 320˚
b) 108˚, 252˚, 288˚
4. a) no
b) no
5.
DE  2 3  2 2
6. a)
b)
sin  
5 26
26
cos  
26
26
sin   
cos  
tan   5
7.
3
5
4
5
tan   
3
4
1
3
3
sin 330o   , cos330o 
, tan 330o  
2
2
3
8. a) QII, positive
c) QIV, negative
4
5
9. a) cos    , tan  
b) QIII, negative
c) QIV, negative
3
4
b) sin  
12
5
, cos   
13
13
Math 20-1
Name: _________________________________
10. a)   225o ,315o
b)   30o , 210o
c)   30o ,330o
11. a)   51o ,129o
b)   144o , 216o
c)   138o ,318o
b) R  70o , Q  7o , PR  1.6cm
12. a) no solution
13. 8.5˚
14. 699 km
15. 12.8 m
16. a) a  21
b) a  21
c) a  21

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