How do you evaluate 1/2 (sin (pi/2) + sin (pi/6))?

1 Answer
Nghi N.
May 15, 2016

3/4

Explanation:

Call the product P = (1/2)p
Apply the trig identity:
sin a + sin b = 2sin ((a + b)/2).cos ((a - b)/2).
We get:
sin ((a + b)/2) --> sin ((pi/2+ pi/6)/2) = sin (pi/3)
cos (a - b)/2 --> cos (pi/2 - (pi)/6)/2 = cos (pi/6)
p = sin pi/2 + sin pi/6 = 2sin(pi/3).cos (pi/6)
Trig table gives -->
sin (pi/3) = sqrt3/2, and cos (pi/6) = sqrt3/2
Therefor,
p = sin (pi/2) + sin (pi/6) = 2(sqrt3/2)(sqrt3)/2 = 3/2
Finally:
P = (1/2)p = (1/2)(3/2) = 3/4

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