1. trigonometry angles.

Hello fellow users, I have 2 questions, thanks in advance!

Question 1:
 Angle z lies in the second quadrant and . Determine an exact value for sin2z.

K, so when I attempted this question, I got 120/169, I am not sure if it is -120/169, or 120/169.

Question 2:

 Given that , and y lies in the third quadrant, express as a difference between
and an angle and then apply a confunction identity to find the measure of y.

I legit have no idea what to do for this!

2. Re: trigonometry angles.

If angle z is in the second quadrant then \displaystyle \displaystyle \begin{align*} \cos{z} \end{align*} can not possibly have been \displaystyle \displaystyle \begin{align*} \frac{12}{13} \end{align*}...

3. Re: trigonometry angles.

Originally Posted by Prove It
If angle z is in the second quadrant then \displaystyle \displaystyle \begin{align*} \cos{z} \end{align*} can not possibly have been \displaystyle \displaystyle \begin{align*} \frac{12}{13} \end{align*}...
I meant -12/13

4. Re: trigonometry angles.

Well you know that in the second quadrant, \displaystyle \displaystyle \begin{align*} \sin{(z)} > 0 \end{align*} and \displaystyle \displaystyle \begin{align*} \cos{(z)} < 0 \end{align*}, so what do you think \displaystyle \displaystyle \begin{align*} \sin{(2z)} = 2\sin{(z)}\cos{(z)} \end{align*} has to be?

5. Re: trigonometry angles.

Originally Posted by Prove It
Well you know that in the second quadrant, \displaystyle \displaystyle \begin{align*} \sin{(z)} > 0 \end{align*} and \displaystyle \displaystyle \begin{align*} \cos{(z)} < 0 \end{align*}, so what do you think \displaystyle \displaystyle \begin{align*} \sin{(2z)} = 2\sin{(z)}\cos{(z)} \end{align*} has to be?
2(5/13)(-12/13)=-120/169? correct?

6. Re: trigonometry angles.

Yes, well done

7. Re: trigonometry angles.

Originally Posted by Prove It
Yes, well done
wow, you teach well, and you are very nice! thanks for the help!