Question

cos theta=7/25, sin theta<0 find sin 2theta

Answer 1

\[
\cos^2(x) + \sin^2(x) = 1\\
\sin( 2 a) = 2 \sin(a) \cos(a)
\]

Answer 2

that is right, but I don't understand what sin (a) is...

Answer 3

\[
\cos^2(\theta) + \sin^2(\theta) = 1\\

\sin^2(\theta) = 1-\cos^2(\theta)\\

\sin^2(\theta) = 1-\left( \frac 7 {25}\right)^2= 1- \frac {49}{625}=\frac{576}{625}
=\left(\frac{24}{25}\right)^2\\
\]

Answer 4

Can you finish it now?

Answer 5

2*(24/25)*(7/25)=.5376
sin theta<0= -.5376
is this right?

Answer 6

No
\[
\sin(\theta) =-\frac{24}{25}
\]

Answer 7

\[
\sin^2(\theta) =
\left(\frac{24}{25}\right)^2\\
\sin(\theta) = \pm \frac {24}{25}

\]

Answer 8

We take the negative side since it was given to be <0

Answer 9

Got it? Can you continue the problem?

Answer 10

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

Answer 11

Yes, I got it.
So then 2*(-24/25)*(7/25)= -336/625

Answer 12

Excellent

Answer 13

Thank you so much for your help! :)