Find the indicated trigonometric value in the specified quadrant.
Function Quadrant Trigonometric Value
$$\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \theta$$
A) $\frac { 2 } { 3 \sqrt { 13 } }$
B) $\frac { 3 \sqrt { 13 } } { 11 }$
C) $\frac { 11 } { 3 \sqrt { 13 } }$
D) $\frac { 2 } { 11 }$
E) Undefined

Question

Quizplus · Accepted Answer

Given $\csc \theta = -\frac{11}{2}$, we know $\sin \theta = -\frac{2}{11}$ because $\csc \theta = \frac{1}{\sin \theta}$. In the fourth quadrant, sine is negative, and cosine is positive. To find $\sec \theta$, we need to find $\cos \theta$ first. Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we get $\cos \theta = \frac{\sqrt{121 - 4}}{11} = \frac{3\sqrt{13}}{11}$. Therefore, $\sec \theta = \frac{1}{\cos \theta} = \frac{11}{3\sqrt{13}}$.

Find the Indicated Trigonometric Value in the Specified Quadrant csc⁡θ=−112 IV sec⁡θ\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \thetacscθ=−211​ IV secθ

Find the Indicated Trigonometric Value in the Specified Quadrant $\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \theta$