use the fundimental identies to find the value of the trigonomic function.
sin 0, if cos 0 = 2/3 and 0 is in quadrant IV
- -3/2
- (3 square root 7)/7
- 5/4
- -( square root 5)/3
Is your 0 supposed to represent $\displaystyle \theta$?
Make use of the Pythagorean Identity:
$\displaystyle \cos^2{\theta} + \sin^2{\theta} = 1$
$\displaystyle \left(\frac{2}{3}\right)^2 + \sin^2{\theta} = 1$
$\displaystyle \frac{4}{9} + \sin^2{\theta} = 1$
$\displaystyle \sin^2{\theta} = \frac{5}{9}$
$\displaystyle \sin{\theta} = \pm \frac{\sqrt{5}}{3}$.
Since $\displaystyle \theta$ is in Quadrant 4, we know $\displaystyle \sin{\theta}< 0$.
So $\displaystyle \sin{\theta} = -\frac{\sqrt{5}}{3}$.