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!