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

Question

Quizplus · Accepted Answer

To express $\cos(\cot^{-1}(u))$ as an algebraic expression, consider a right triangle where the cotangent of an angle is $u$, meaning the adjacent side over the opposite side is $u$. This makes the adjacent side $u$ and the opposite side $1$. The hypotenuse, using the Pythagorean theorem, is $\sqrt{u^2 + 1}$. Cosine is the adjacent side over the hypotenuse, so $\cos(\cot^{-1}(u)) = \frac{u}{\sqrt{u^2 + 1}}$.

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

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