If cot theta= 4/3, find csc theta

Question

asked May 11, 2020 166k views

1 Answer

Shahab Rauf · Answer 1 · 2020-05-16T02:22:28+0000

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:

$√(csc^2\theta)=\±\sqrt{(25)/(9)}$

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