Question

If sin theta=3/5 and theta has its terminal side in Quadrant II, find the exact value of tan 2 theta.

Answer 1

So would this just be tan(2 theta)=2*sin(theta)*tan(theta)?

Answer 2

Or am I going about this wrong?

Answer 3

if it were sin(2theta), then you'd be correct

Answer 4

look at this pdf

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 5

look at the `Double Angle Formulas` on page 2

Answer 6

Oh LOL

Answer 7

I know that tan would be 3/4...So, I just plug that in for theta?

Answer 8

you replace every `tan(theta)` with 3/4

Answer 9

I'm confused...so the numerator would just be 2(3/4)?

Answer 10

or 2tan(3/4)?

Answer 11

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


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


\[\Large \tan(2\theta) = \frac{2*({\color{red}{\tan(\theta)}})}{1-({\color{red}{\tan(\theta)}})^2}\]


\[\Large \tan(2\theta) = \frac{2*({\color{red}{3/4}})}{1-({\color{red}{3/4}})^2}\]


\[\Large \tan(2\theta) = ???\]

Answer 12

Ohhh

Answer 13

(3/2)/(1-(9/16)) right?

Answer 14

yes, now simplify as much as possible

Answer 15

Okay

Answer 16

24/7?

Answer 17

I'm getting the same

Answer 18

actually hold on

Answer 19

I'm just realizing that theta is in Q2

Answer 20

tangent is negative in Q2

Answer 21

so -24/7? LOL

Answer 22

correct

Answer 23

Awesome, again, thank you for the help!

Answer 24

glad to be of help

Answer 25

:)