How do you evaluate cos((7pi)/6+pi/4)?

1 Answer
Nghi N.
Apr 7, 2016

((sqrt2)(1 - sqrt3))/4

Explanation:

Apply trig identity: cos (a + b) = cos a.cos b - sin a.sin b
cos ((7pi)/6 + (pi)/4) = cos ((7pi)/6).cos (pi/4) - sin (pi/4).sin ((7pi)/6)
Trig table gives and trig unit circle give-->
cos (pi/4) = sqrt2/2; sin (pi/4) = sqrt2/2
cos ((7pi)/6) = - cos (pi/6) = - sqrt3/2
sin ((7pi)/6) = - sin (pi/6) = -1/2
Therefor,

cos ((7pi)/6 + pi/4) = (-sqrt3/2)(sqrt2/2) - (sqrt2/2)(-1/2) =
= ((sqrt2)(1 - sqrt3))/4

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