1. ## double angle problem

It says the sinx=$\displaystyle 14/15$ and it is in quadrant 2
what quadrant is the sin2x in?
(NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

i really need help fast thnx

2. Originally Posted by brianH
It says the sinx=$\displaystyle 14/15$ and it is in quadrant 2
what quadrant is the sin2x in?
(NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

i really need help fast thnx
$\displaystyle \sin(2x)=2\sin(x)\cos(x)=2\cdot \frac{14}{15}\cdot \frac{\sqrt{29}}{15}$

3. i got that and it was $\displaystyle -28 \frac{\sqrt{29}}{225}$
but how do i fugure out what quad thats in

4. Originally Posted by brianH
It says the sinx=$\displaystyle 14/15$ and it is in quadrant 2
what quadrant is the sin2x in?
(NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

i really need help fast thnx
We will use the identity $\displaystyle sin(2x)=2sinxcosx$ to help us. Since $\displaystyle sinx=\frac{14}{15}$, we can determine that $\displaystyle cosx=\frac{-\sqrt{29}}{15}$ (since sine was defined in the 2nd quadrant). Plugging this into the identity, we have:

$\displaystyle sin(2x)=2{\left(\frac{14}{15}\right)}{\left(\frac{-\sqrt{29}}{15}\right)}=\frac{-28\sqrt{29}}{225}$.

I'm going to conclude that $\displaystyle sin2x$ falls in the 4th quadrant, since $\displaystyle sin\theta=\frac{opp}{adj}$. Since the opposite is negative, it will reside either in the 3rd or 4th quadrants. Since the adjacent is positive, it will reside in the 1st or 4th quadrants. Thus, the value of $\displaystyle sin2x=\frac{-28\sqrt{29}}{225}$ satisfies the conditions for it to be in the 4th quadrant.

Hope this helped you out!

5. Originally Posted by TheEmptySet
$\displaystyle \sin(2x)=2\sin(x)\cos(x)=2\cdot \frac{14}{15}\cdot \frac{\sqrt{29}}{15}$
I'm sure you're missing a negative for the cosine term. Sine is positive in the second quadrant, whereas cosine is negative!

6. thnx, it was a question on a test that i have to finish tomorrow at school

7. Originally Posted by Chris L T521
I'm sure you're missing a negative for the cosine term. Sine is positive in the second quadrant, whereas cosine is negative!
Thanks I remembered while I was washing some dishes that I forgot to check what quadrants it was in.

Sorry

8. hehe! I always forget the quadrant!