Answer
See explanation.
Work Step by Step
By definition, $sin\theta=\frac{opposite}{hypotenuse}$ and $sec\theta=\frac{hypotenuse}{adjacent}$, draw a right triangle with a hypotenuse of $5$ and an opposite side of $4$. We have $sin\theta=\frac{4}{5}$ and we can find the adjacent side as $3$. Thus $sec(sin^{-1}\frac{4}{5})=sec\theta=\frac{5}{3}$
