Find the exact value of the expression, if possible. Do not use a calculator.
-$\cot \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$
A) 1
B) $\sqrt { 2 }$
C) $\frac { \sqrt { 2 } } { 2 }$
D) 2 Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function.

Question

Quizplus · Accepted Answer

The expression $\cot \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$ can be solved by considering a right triangle where the opposite side over the hypotenuse is $\frac{\sqrt{2}}{2}$, which corresponds to an angle of 45 degrees or $\frac{\pi}{4}$ radians. The cotangent of this angle, which is the ratio of the adjacent side to the opposite side, is 1.

Find the Exact Value of the Expression, If Possible cot⁡(sin⁡−122)\cot \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)cot(sin−122​​)

Find the Exact Value of the Expression, If Possible $\cot \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$