Degree to Radian

Degrees and Radians

What is a radian?

• the central angle associated with a circle sector that has equal length radius and arc

• approximately 57.3 degrees

Angle Movement and Location

Converting Radians to degrees

Conversion Factors

To keep EXACT answers don't approximate PI treat it like a variable and either cancel it off, or it should be part of your answer

Converting Hints

• If you convert from Degrees, pi will show up in your answer for radians....

• Leave Pi as a symbol in radians! (unless you need a decimal answer)

• If you converting from Radians, pi will cancel out

Converting 200 degrees to radians

​Converting Radians to Degrees

Finding Reference Angles

• The blue portion of graph is the original angle

• The red portion is reference angle

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Reference Angle

• Measure of Terminal side to closest x axis

• Distance to x axis

• MUST be < 90 degree

• MUST be Positive

Finding Reference angle by Quadrant

• Quadrant 1 - itself

• Quadrant 2 - 180 Degrees minus the angle

• Quadrant 3 - The angle minus 180 degrees

• Quadrant 4 - 360 minus the angle

Fill in the Blanks

Convert $\frac{3\pi}{2}$  radians to degrees.

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Convert 288 degrees to radian.

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Convert 8 radians to degrees.

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Convert 400 degrees to radian.

Multiple Choice

Convert 30 degrees to radians

• $$\frac{\pi}{2}radians$$

• $$\frac{\pi}{3}radians$$

• $$\frac{\pi}{4}radians$$

• $$\frac{\pi}{6}radians$$

• none of these

Multiple Choice

Convert 45 degrees to radians

• $$\frac{\pi}{2}radians$$

• $$\frac{\pi}{3}radians$$

• $$\frac{\pi}{4}radians$$

• $$\frac{\pi}{6}radians$$

• none of these

Multiple Choice

Convert 60 degrees to radians

• $$\frac{\pi}{2}radians$$

• $$\frac{\pi}{3}radians$$

• $$\frac{\pi}{4}radians$$

• $$\frac{\pi}{6}radians$$

• none of these

Multiple Choice

What is the reference angle?

• 112

• 68

• 158

• 248

Multiple Choice

What is the reference angle?

• 43

• -43

• 47

• -47

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°