Use identities to fill in the blank with the appropriate trigonometric function name.
-Find $\cos \theta$ if $\tan \theta = 4$ and $\sin \theta

Question

Use identities to fill in the blank with the appropriate trigonometric function name.
-Find $\cos \theta$ if $\tan \theta = 4$ and $\sin \theta < 0$.
A) $- 17$
B) $\frac { 1 } { 4 }$
C) $- \frac { \sqrt { 17 } } { 17 }$
D) $- \frac { \sqrt { 17 } } { 4 }$

Quizplus · Accepted Answer

Given $\tan \theta = 4$, we can represent this as $\frac{\sin \theta}{\cos \theta} = \frac{4}{1}$. Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we substitute $\sin \theta = 4\cos \theta$ and solve for $\cos \theta$, finding $\cos \theta = - \frac { \sqrt { 17 } } { 17 }$ when considering $\sin \theta < 0$.

Use Identities to Fill in the Blank with the Appropriate cos⁡θ\cos \thetacosθ

Use Identities to Fill in the Blank with the Appropriate $\cos \theta$