Question

For the rotation -58°, find the coterminal

angle from 0° ≤ theta < 360°, the quadrant, and
the reference angle.


The coterminal angle is___ degrees, in Quadrant____ with a reference angle of____ degrees

Answer 1

To find coterminal angles, add integer multiples of
`360^(\circ)`.

Adding
`-58^(\circ)+360^(\circ)=\boxed{302^(\circ)}`.

Since this angle is between
`270^(\circ)` and
`360^(\circ)`, it lies in Quadrant IV.

Hence, the reference angle is
`360^(\circ)-\theta=\boxed{58^(\circ)}`.