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

Question

Quizplus · Accepted Answer

To express $\cos \left( \cot ^ { - 1 } \mathrm { u } \right)$ as an algebraic expression, consider a right triangle where the cotangent of an angle is $u$, meaning $\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}} = u$. This implies the adjacent side is $u$ and the opposite side is $1$. Using the Pythagorean theorem, the hypotenuse is $\sqrt{u^2 + 1}$. Therefore, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{u}{\sqrt{u^2 + 1}}$, making option A correct.

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 $\cos \left( \cot ^ { - 1 } \mathrm { u } \right)$