Any angle trigonometry function example
Question:
a is an angle in Quadrant II, and sin a = 1/3. Find the value of sin (a + pi/2).
Solution:
- sin (a + pi/2) = sin (pi/2 + a) = cos a
- using the formula: sin2a + cos2a = 1
- cos2a = 1 - sin2a = 1 - (1/3)2 = 1 - 1/9 = 8/9
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 r2 = x2 + y2. 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.