Calculate cos a if sin a = 2/3 and a is in the second quadrant.

First, we have to emphasize that if a is in the second
quadrant, the value of cos a is negative.

Due to the fact
that the value of sin a is given, from enunciation, we'll calculate the value of cos a,
with the help of fundamental formula of trigonometry:

(sin
a)^2 + (cos a)^2 = 1

But sin a =
2/3

(2/3)^2 +  (cos a)^2 =
1

We'll subtract (2/3)^2 both
sides:

(cos a)^2 = 1 - 4/9

cos
a = -sqrt (5/9)

cos a = -(sqrt
5)/3