Question

Coterminal angle help

Answer 1

Answer:
`\bold{(3\pi)/(2)}`

Explanation:

Coterminal means it is in the same place on the Unit Circle but one or more rotations clockwise or counterclockwise.

Note: one rotation is 2π (which is equivalent to
`(4\pi)/(2)`)

`-(13\pi)/(2)+(4\pi)/(2)=-(9\pi)/(2)\\\\.\qquad\qquad\quad=-(9\pi)/(2)+(4\pi)/(2)=-(5\pi)/(2)\\\\.\qquad\qquad\qquad\qquad\qquad\quad=-(5\pi)/(2)+(4\pi)/(2)=-(\pi)/(2)\\\\.\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad=-(\pi)/(2)+(4\pi)/(2)=(3\pi)/(2)\\\\\\(3\pi)/(2)\text{ is between 0 and }2\pi\text{ so this is the angle we are looking for!}`