Question

An angle's terminal ray sweeps out 169 degrees, and then an additional 1.5 radians.This angle sweeps out what percent of a full rotation? %   What is the radian measure of this angle? radians   What is the degree measure of this angle? degrees   

Answer 1

Input Data

An angle's terminal ray sweeps out 169 degrees, and then an additional 1.5 radians.

Procedure

A.

First let's convert radians to degrees

$1.5\text{ rad}\cdot\frac{180}{\pi}=86\~$

The total swept angle would be

$169+86=255$

A full rotation is equal to 360

$\frac{255}{360}=70.83\text{ \%}$

B.

Now let's convert the total angle in radians

$255\cdot\frac{\pi}{180}=4.45\text{ rads}$

C.

The angle in degrees is 255°