Answer:
sin (theta) = [tex]\frac{\sqrt{5} }{3}[/tex]
Step-by-step explanation:
cos = adjacent side/hypotenuse
Then, in a right triangle the adjacent = 2 and the hypotenuse = 3
By the Pythagorean theorem, 3^2 = 2^2 + opposite side^2
9 - 4 = 5
opposite side = [tex]\sqrt{5}\\[/tex]
sin (theta) = [tex]\frac{\sqrt{5} }{3}[/tex]
An easier way is to find sin(arccos (-2/3) = [tex]\frac{\sqrt{5} }{3}[/tex]
Note: Remember that the sin is positive in the 2nd quadrant.
