Find $\tan 2 x$ , given that $\sin x = \frac { 3 } { 5 }$ and $x$ is in quadrant II
A) $- 24$

B) $- \frac { 24 } { 7 }$

C) $\frac { 4 \sqrt { 6 } } { 7 }$

D) $\frac { \sqrt { 6 } } { 7 }$

E) $- \frac { 4 } { 7 }$

Question

Find $\tan 2 x$ , given that $\sin x = \frac { 3 } { 5 }$ and $x$ is in quadrant II
A) $- 24$

B) $- \frac { 24 } { 7 }$

C) $\frac { 4 \sqrt { 6 } } { 7 }$

D) $\frac { \sqrt { 6 } } { 7 }$

E) $- \frac { 4 } { 7 }$

Quizplus · Accepted Answer

To find $\tan 2x$, we can use the double angle formula for tangent, $\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$. Since $\sin x = \frac{3}{5}$ and $x$ is in the second quadrant, we can find $\cos x$ using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, which gives $\cos x = -\frac{4}{5}$ (negative because cosine is negative in the second quadrant). Then, $\tan x = \frac{\sin x}{\cos x} = \frac{3/5}{-4/5} = -\frac{3}{4}$. Plugging this into the double angle formula gives $\tan 2x = \frac{2(-\frac{3}{4})}{1 - (-\frac{3}{4})^2} = \frac{-\frac{3}{2}}{1 - \frac{9}{16}} = \frac{-\frac{3}{2}}{\frac{7}{16}} = -\frac{24}{7}$.

Find tan⁡2x\tan 2 xtan2x , Given That sin⁡x=35\sin x = \frac { 3 } { 5 }sinx=53​

Find $\tan 2 x$ , Given That $\sin x = \frac { 3 } { 5 }$