18
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
-Find $\tan \theta$, given that $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.
A) $\frac { 5 } { 4 }$
B) $- \frac { 3 \sqrt { 7 } } { 7 }$
C) $- \frac { 3 } { 2 }$
D) $- \frac { \sqrt { 7 } } { 9 }$

Question

Quizplus · Accepted Answer

In quadrant II, sine is positive and cosine is negative. Given $\sin \theta = \frac{3}{4}$, we can use the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$ to find $\cos \theta$. Solving for $\cos \theta$, we get $\cos \theta = -\frac{\sqrt{7}}{4}$. Therefore, $\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{3}{4}}{-\frac{\sqrt{7}}{4}} = -\frac{3\sqrt{7}}{7}$.

18 Suppose That Is in Standard Position and the Given tan⁡θ\tan \thetatanθ

18
Suppose That Is in Standard Position and the Given $\tan \theta$