If $\sin(\theta) = -\frac{2}{\sqrt{13}}$ and $\cos(\theta) > 0$, find the exact values for the other 5 functions:\[\cos(\theta) = \]\[\tan(\theta) = \]\[\csc(\theta) = \]\[\sec(\theta) = \]\[\cot(\theta) = \]

Answered: if Sin(t)==

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

If $\sin(\theta) = -\frac{2}{\sqrt{13}}$ and $\cos(\theta) > 0$, find the exact values for the other 5 functions:

\[
\cos(\theta) =
\]

\[
\tan(\theta) =
\]

\[
\csc(\theta) =
\]

\[
\sec(\theta) =
\]

\[
\cot(\theta) =
\]

Expert Solution

Step 1

Given
$\sin t = - \frac{2 \sqrt{13}}{13}$ , we know that the sint is -ve in III and IV quadrant .
$\cos t > 0$ , we know that the cost is +ve in IV and I quadrant.

So t lines in the IV quadrant.
$\cos t = \sqrt{1 - \sin^{2} t} \cos t = \sqrt{1 - {(- \frac{2 \sqrt{13}}{13})}^{2}} \cos t = \sqrt{1 - \frac{4}{13}} \cos t = \sqrt{\frac{9}{13}} = \frac{3}{\sqrt{13}}$