Given that $\cos \theta = \frac { 14 } { 15 }$, find $\csc \theta$.
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$; then use the Pythagorean Theorem to determine the third side.)
A) $\frac { \sqrt { 29 } } { 15 }$
B) $\frac { 15 } { 14 }$
C) $\frac { 14 } { \sqrt { 29 } }$
D) $15 \sqrt { 29 }$
E) $\frac { 15 } { \sqrt { 29 } }$

Question

Quizplus · Accepted Answer

Given $\cos \theta = \frac{14}{15}$, we can represent this in a right triangle as the adjacent side over the hypotenuse. Using the Pythagorean theorem, the opposite side can be found as $\sqrt{15^2 - 14^2} = \sqrt{225 - 196} = \sqrt{29}$. The cosecant ($\csc$) function is the reciprocal of the sine function, which is opposite over hypotenuse, so $\csc \theta = \frac{15}{\sqrt{29}}$.

Given That cos⁡θ=1415\cos \theta = \frac { 14 } { 15 }cosθ=1514​

Given That $\cos \theta = \frac { 14 } { 15 }$