How do you evaluate cos ((3pi)/8)?

1 Answer
Nghi N.
May 8, 2016

sqrt(2 - sqrt2)/2

Explanation:

Property of complementary arcs -->
cos ((3pi)/8) = cos (-pi/8 + pi/2) = sin (pi/8).
Evaluate sin (pi/8) by applying the trig identity:
cos 2a = 1 - 2sin^2 a.
Trig table -->
cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8).
2sin^2 (pi/8) = 1 - sqrtt2/2 = (2 - sqrt2)/2
sin^2 (pi/8) = (2 - sqrt20/4
sin (pi/8) = sqrt(2 - sqrt2)/2
Since pi/8 is in Quadrant I, then we select the positive value.
cos ((3pi)/8) = sin (pi/8) = sqrt(2 - sqrt2)/2

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