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Angle Conversion in Coordinate Systems Worksheet

Grade 12 Math worksheet on converting angles between degrees and radians, and representing them in various coordinate systems.

Grade 12 Math GeometryAngle Conversion in Coordinate Systems
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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.D.9CCSS.MATH.CONTENT.HSG.SRT.D.10CCSS.MATH.CONTENT.HSG.SRT.D.11

Topics

MathGeometryTrigonometryAnglesDegreesRadiansCoordinate Systems
7 sections · Free to use · Printable
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Angle Conversion in Coordinate Systems

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Date:

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Read each question carefully and provide accurate answers. Show all your work for full credit.

1. Convert 210° to radians.

a

7π/6 radians

b

5π/6 radians

c

7π/12 radians

d

11π/6 radians

2. Convert 3π/4 radians to degrees.

a

120°

b

135°

c

150°

d

225°

3. An angle of 360° is equivalent to   radians.

4. The unit circle has a radius of  .

5. Draw an angle of 45° in standard position on a coordinate plane and label its terminal side.

-5-4-3-2-112345-5-4-3-2-112345

6. Explain the relationship between the arc length, radius, and central angle in radians.

7. A positive angle is measured clockwise from the positive x-axis.

T

True

F

False

8. An angle of -90° is coterminal with an angle of 270°.

T

True

F

False

9. A bicycle wheel has a radius of 30 cm. If the wheel rotates through an angle of 5π/3 radians, what is the distance traveled by a point on the rim of the wheel?

10. An object travels along a circular path with a radius of 10 meters. If it sweeps out an angle of 150°, what is the area of the sector formed by its path?