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# A circle has an arc of length 32π that is intercepted by a central angle of 240. What is the radius of the circle?

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A circle has an arc of length 32π that is intercepted by a central angle of 240°.
What is the radius of the circle?

A circle has a radius of 48 millimeters.
What is the central angle in radians, that intercepts an arc of length 36π millimeters?

A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant IV.

Select from the drop-down menus to correctly complete each statement.

The cosine of the angle is Choose...negative OR positive.

The sine of the angle is Choose...negative OR positive.

Guest Jan 11, 2018
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32pi  =  2*pi *r* (240/ 360)        divide both sides by pi

32  =   2 * (240/360) * r

32  = 240/180 * r

32  =  (4/3) * r

(32) (3/4)   = r

24  =  r

36pi  =  2* pi * 48  *  ( Angle / 360)

36    = (96/360)  * Angle

36 (360 / 96)  = Angle

(36/96)(360)  = Angle

(3/8)(360)  - Angle

135°  = Angle  =   (3/4)pi   rads

Quadrant iV ⇒  cosine positive, sine negative

CPhill  Jan 11, 2018

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