Question

If cot theta= 4/3, find csc theta

Answer 1

Answer: Option d.

Explanation:

The trigonometric identity needed is:

`csc^2\theta=cot^2\theta+1`

Knowing that
`cot\theta=(4)/(3)`:

Substitute it into
`csc^2\theta=cot^2\theta+1`:

`csc^2\theta=((4)/(3))^2+1`

Simplify the expression:

`csc^2\theta=((4)/(3))^2+1\\\\csc^2\theta=(16)/(9)+1\\\\csc^2\theta=(25)/(9)`

Solve for
`csc\theta`. Apply square root at both sides of the expression:

`√(csc^2\theta)=\±\sqrt{(25)/(9)}`

`csc\theta=(5)/(3)`