precalculus
bdadio
precalc6.docx1. Fill in the blank.
Two angles that have the same initial and terminal sides are .
2. Fill in the blank.
One is the measure of a central angle that intercepts an arc equal in length to the radius of the circle.
3. What is the sum of two complementary angles? °
4. Are the angles 300° and −210° coterminal?
YesNo
5. Is the angle
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4π |
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5 |
acute or obtuse?
acuteobtuse
6. Determine the quadrant in which each angle lies.
(a) 154°
III IIIIV
(b) 199°
III IIIIV
7. Determine the quadrant in which each angle lies.
(a) 61.3°
III IIIIV
(b) 222.3°
III IIIIV
8. Sketch each angle in standard position.
(a)
−90°
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(b)
−60°
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9. Sketch each angle in standard position.
(a)
−810°
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(b)
−570°
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10. Determine two coterminal angles in degree measure (one positive and one negative) for each angle. (There are many correct answers.)
(a)
−445°
θ = ° (negative angle) θ = ° (positive angle) (b) 230° θ = ° (negative angle) θ = ° (positive angle)
11. Find (if possible) the complement and supplement of the angle. (Enter NONE in any unused answer blanks.)
123°
° (complement) ° (supplement)
12. Find (if possible) the complement and supplement of each angle. (Enter NONE in any unused answer blanks.)
(a) 78° ° (complement) ° (supplement) (b) 166° ° (complement) ° (supplement)
13. Find (if possible) the complement and supplement of the angle. (Enter NONE in any unused answer blanks.)
157°
° (complement) ° (supplement)
14. Determine the quadrant in which each angle lies. (The angle is given in radians.)
(a)
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7π |
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4 |
Quadrant IQuadrant II Quadrant IIIQuadrant IV
(b)
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11π |
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4 |
Quadrant IQuadrant II Quadrant IIIQuadrant IV
15. Determine the quadrant in which each angle lies. (The angle measure is given in radians.)
(a)
−
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5π |
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12 |
first quadrantsecond quadrant third quadrantfourth quadrant
(b)
−
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11π |
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9 |
first quadrantsecond quadrant third quadrantfourth quadrant
16. Sketch each angle in standard position.
(a)
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4π |
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5 |
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(b)
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5π |
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4 |
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17. Sketch each angle in standard position.
(a)
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11π |
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6 |
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(b)
−
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4π |
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5 |
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18. Rewrite each angle in radian measure as a multiple of π. (Do not use a calculator.)
(a)
225°
rad (b)
300°
rad
19. Rewrite each angle in degree measure. (Do not use a calculator.)
(a)
−
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7π |
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2 |
° (b)
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29π |
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15 |
°
20. Convert the angle measure from radians to degrees. Round to three decimal places.
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2π |
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15 |
°
21. Find (if possible) the complement and supplement of the angle. (Enter NONE in any unused answer blanks.)
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5π |
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6 |
(complement) (supplement)
22. Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)
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Radius r |
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Central Angle θ |
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Arc Length s |
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8 centimeters |
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radians |
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centimeters |
23. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
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Radius r |
Arc Length s |
Central Angle θ |
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17 feet |
10 feet |
radians |
