Answer: Option d.
Step-by-step explanation:
The trigonometric identity needed is:
[tex]csc^2\theta=cot^2\theta+1[/tex]
Knowing that [tex]cot\theta=\frac{4}{3}[/tex]:
Substitute it into [tex]csc^2\theta=cot^2\theta+1[/tex]:
[tex]csc^2\theta=(\frac{4}{3})^2+1[/tex]
Simplify the expression:
[tex]csc^2\theta=(\frac{4}{3})^2+1\\\\csc^2\theta=\frac{16}{9}+1\\\\csc^2\theta=\frac{25}{9}[/tex]
Solve for [tex]csc\theta[/tex]. Apply square root at both sides of the expression:
[tex]\sqrt{csc^2\theta}=\±\sqrt{\frac{25}{9}}[/tex]
[tex]csc\theta=\frac{5}{3}[/tex]
