Question

Answer the following. (a) Find an angle between 0 and 2π that is coterminal with 19π/6. (b) Find an angle between 0° and 360° that is coterminal with -300°. Give exact values for your answers.(a) radians(b)

Answer 1

Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. In radians, given an angle theta, its coterminal angles are given by:

`\theta\pm2\pi`

In our problem, we want to find a coterminal angle to 19π/6 on the interval between 0 and 2π. If we subtract 2π from this angle, we're going to find the coterminal angle on this interval:

`(19\pi)/(6)-2\pi=(19\pi)/(6)-(12\pi)/(6)=((19-12)\pi)/(6)=(7\pi)/(6)`

The coterminal angle is 7π/6.

In degrees, given an angle theta, its coterminal angles are given by:

`\theta\pm360^o`

We want to find an angle between 0° and 360° that is coterminal with -300°, therefore, we must add 360º to our angle:

`-300^o+360^o=60^o`

The coterminal angle to -300º between 0º and 360º is 60º.