Find an algebraic expression that is equivalent to the expression.. $$\tan \left( \arccos \frac { x } { 6 } \right)$$
A) $\frac { \sqrt { 36 - x ^ { 2 } } } { x }$
B) $\frac { 36 - x ^ { 2 } } { x }$
C) $\frac { \sqrt { 36 + x ^ { 2 } } } { x }$
D) $\frac { \sqrt { 36 + x ^ { 2 } } } { 36 + x ^ { 2 } }$
E) $\frac { \sqrt { 36 - x ^ { 2 } } } { 36 - x ^ { 2 } }$

Question

Find an algebraic expression that is equivalent to the expression..​ $$\tan \left( \arccos \frac { x } { 6 } \right)$$ ​
A) $\frac { \sqrt { 36 - x ^ { 2 } } } { x }$
B) $\frac { 36 - x ^ { 2 } } { x }$
C) $\frac { \sqrt { 36 + x ^ { 2 } } } { x }$
D) $\frac { \sqrt { 36 + x ^ { 2 } } } { 36 + x ^ { 2 } }$
E) $\frac { \sqrt { 36 - x ^ { 2 } } } { 36 - x ^ { 2 } }$

Quizplus · Accepted Answer

To find an expression equivalent to $\tan(\arccos(\frac{x}{6}))$, consider a right triangle where the adjacent side to the angle is $x$ and the hypotenuse is $6$. The opposite side, by the Pythagorean theorem, is $\sqrt{6^2 - x^2} = \sqrt{36 - x^2}$. Thus, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{36 - x^2}}{x}$.

Find an Algebraic Expression That Is Equivalent to the Expression tan⁡(arccos⁡x6)\tan \left( \arccos \frac { x } { 6 } \right)tan(arccos6x​)

Find an Algebraic Expression That Is Equivalent to the Expression $\tan \left( \arccos \frac { x } { 6 } \right)$