Because the angle a is an angle of Quadrant II, then the terminal side of the angle a lies in Quadrant II. P (x, y) is a point lies on the terminal side of the angle a. Since the
point P lies in the Quadrant II, so the x-coordinate of the point P is a value of negative and the y-coordinate of the point P is a value of positive. By definition, cos a = x/r,
in which r^{2} = x^{2} + y^{2}. The value of r is always positive. So, if the angle a is an angle of Quadrant II, then the value of cos a is negative.

cos a = - Sqrt (8/9) = -2 Sqrt (2)/3

Therefore, the value of sin (a + pi/2) is equal to -2 Sqrt (2)/3. Please watch the video for more detail.