Question

If cot theta= 4/3, find csc theta

Answer 1

Answer: Option d.

Step-by-step explanation:

The trigonometric identity needed is:

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

Knowing that $cot\theta=\frac{4}{3}$:

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

$csc^2\theta=(\frac{4}{3})^2+1$

Simplify the expression:

$csc^2\theta=(\frac{4}{3})^2+1\\\\csc^2\theta=\frac{16}{9}+1\\\\csc^2\theta=\frac{25}{9}$

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

$\sqrt{csc^2\theta}=\±\sqrt{\frac{25}{9}}$

$csc\theta=\frac{5}{3}$