Question

Use the given information to find the exact value of the expression.

sin θ = 24/25, θ lies in quadrant II Find tan 2θ.
A. - 526/527
B.336/625
C. -336/527
D. 336/527

Answer 1

@Michele_Laino Last one help me ? /.\

Answer 2

well draw a diagram



then us the fact that

\[\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}\]

Answer 3

from your data, we have that cos (theta)<0 bein theta in the II quadrant, and all points i the second quadrant have the x-coordinate <0,
so:
\[\cos \theta=-\sqrt{1-\frac{ 24^{2} }{ 25^{2} }}=-\frac{ 7 }{ 5 }\]

Answer 4

Now, we have:
\[\tan \theta=\frac{ \sin \theta }{ \cos \theta }=\frac{ 24/25 }{ -7/25 }=-\frac{ 24 }{ 7 }\]

Answer 5

So my answer is either a or c ?

Answer 6

Sorry, I have made an error:
\[\cos \theta=-\frac{ 7 }{ 25 }\]
and using the subsequent formula:
\[\tan(2\theta)=\frac{ 2\tan \theta }{ 1-(\tan )^{?} }\]
you get \[\frac{ 48*7 }{ 31*17 }=...\]

Answer 7

So D.

Answer 8

thank you !!!!!

Answer 9

thank you!

Answer 10

if you look at the diagram a = -7

so then

tan(theta) = -24/7

then

using the double angle for tan

\[\tan(2 \theta) = \frac{-\frac{24}{7}}{1 - (-\frac{24}{7})^2}\]

just calculate it out

Answer 11

oops double the numerator

Answer 12

Sorry tI have too hurry before, the exact formula is:
\[\tan(2\theta)=\frac{ 2 \tan \theta }{ 1-(\tan \theta) ^{2}}\]