Write the trigonometric expression as an algebraic expression in u.
-$\sec \left( \sin ^ { - 1 } u \right)$
A) $\sqrt { 1 - u ^ { 2 } }$
B) $\frac { 1 } { \sqrt { 1 - u ^ { 2 } } }$
C) $\frac { 1 } { \sqrt { u ^ { 2 } - 1 } }$
D) $\frac { \sqrt { \mathrm { u } ^ { 2 } - 1 } } { \mathrm { u } }$

Question

Quizplus · Accepted Answer

The expression $\sec(\sin^{-1}u)$ can be understood by considering a right triangle where the sine of an angle is $u$, meaning $u$ is opposite/hypotenuse. The secant is the reciprocal of the cosine, which is hypotenuse/adjacent. Using the Pythagorean theorem, the adjacent side is $\sqrt{1-u^2}$, making the expression $\frac{1}{\sqrt{1-u^2}}$.

Write the Trigonometric Expression as an Algebraic Expression in U sec⁡(sin⁡−1u)\sec \left( \sin ^ { - 1 } u \right)sec(sin−1u)

Write the Trigonometric Expression as an Algebraic Expression in U $\sec \left( \sin ^ { - 1 } u \right)$