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

#1**+2 **

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