Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\sin \theta = \frac { 6 } { 7 } ; \cot \theta$
A) $\frac { \sqrt { 13 } } { 7 }$
B) $\frac { 6 } { \sqrt { 13 } }$
C) $\frac { \sqrt { 13 } } { 6 }$
D) $\frac { 7 } { \sqrt { 13 } }$

Question

Quizplus · Accepted Answer

Given $\sin \theta = \frac{6}{7}$, we can find $\cot \theta$ by first finding $\cos \theta$. In a right triangle, if $\sin \theta = \frac{6}{7}$, then the opposite side is 6, the hypotenuse is 7, and the adjacent side (using Pythagoras' theorem) is $\sqrt{7^2 - 6^2} = \sqrt{49 - 36} = \sqrt{13}$. Thus, $\cos \theta = \frac{\sqrt{13}}{7}$, and $\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{\sqrt{13}/7}{6/7} = \frac{\sqrt{13}}{6}$.

Assume That θ \theta θ Is an Acute Angle in a Right Triangle Satisfying the a Right

Assume That $\theta$ Is an Acute Angle in a Right Triangle Satisfying the a Right