Use the figure below to find the exact value of the given trigonometric expression.
$\cot \frac { x } { 2 }$

A) $\cot \frac { x } { 2 } = \frac { \sqrt { 2 } } { 10 }$

B) $\cot \frac { x } { 2 } = \frac { 1 } { 7 }$

C) $\cot \frac { x } { 2 } = 7$

D)$\cot \frac { x } { 2 } = \frac { 7 \sqrt { 2 } } { 10 }$

E)$\cot \frac { x } { 2 } = \frac { 7 } { 12 }$

Question

Use the figure below to find the exact value of the given trigonometric expression.
$\cot \frac { x } { 2 }$

A) $\cot \frac { x } { 2 } = \frac { \sqrt { 2 } } { 10 }$

B) $\cot \frac { x } { 2 } = \frac { 1 } { 7 }$

C) $\cot \frac { x } { 2 } = 7$

D)$\cot \frac { x } { 2 } = \frac { 7 \sqrt { 2 } } { 10 }$

E)$\cot \frac { x } { 2 } = \frac { 7 } { 12 }$

Quizplus · Accepted Answer

The cotangent of an angle is the reciprocal of its tangent. If the figure (which is not visible in this question) shows a right triangle or provides enough information to find the sine and cosine of $x/2$, then $\cot(x/2)$ can be calculated directly or through trigonometric identities. Without the figure, we cannot directly calculate the value, but given the options, if the correct approach involves using known trigonometric identities or properties that lead to a specific numerical result, option C ($\cot \frac{x}{2} = 7$) could be correct based on the assumption that it involves the reciprocal relationship of tangent and cotangent, and possibly the half-angle formulas. However, without the figure or additional context, this explanation is speculative and based on the structure of typical trigonometry problems.

Use the Figure Below to Find the Exact Value of the Given