Question

If sin theta = 2/3 (and it does believe me) and theta is in II (I think that means quadrant two?) find sin 2 theta.

Answer 1

first you need to find \(\cos(\theta)\) by pythgoras

Answer 2

then use
\[(\sin(2\theta)=2\sin(\theta)\cos(\theta)\]

Answer 3

Wait so you're saying I should draw a triangle first.

Answer 4

\[\sin(\theta)=\frac{2}{3}\implies\cos(\theta)=-\frac{\sqrt{5}}{3}\] the minus sign because you are in quadrant II

Answer 5

then plug in to formula above and you are done

Answer 6

you said it was that is how

Answer 7

Haha I know. I just realized.

Answer 8

If sin theta = 2/3 (and it does believe me)

Answer 9

so i went from there
notice that we are not required to find \(\theta\)

Answer 10

Now I have a question. This is quadrant two right?

Answer 11

yes. and there sine is positive (because you are up) and cosine is negative (because you are to the left)

Answer 12

Now hold on a second what does cos have to do with anything?

Answer 13

You're saying I should just multiply that cosine stuff with two?

Answer 14

yup

Answer 15

\[-2\times \frac{2}{3}\times \frac{\sqrt{5}}{3}\]

Answer 16

or if you prefer
\[-\frac{4\sqrt{5}}{9}\]