how to evaluate cos13pi/6 and sin37pi/4?

Expert Answers

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We have to evaluate cos 13pi/6 and sin 37pi/4

Now cos (x+ 2*pi) = cos x

cos 13pi/6 = cos ( pi/6 + 2*pi) = cos (pi/6) = sqrt 3 / 2

sin (x + pi) = -sin x

sin ( 37*pi/4) = sin (36*pi/4 + pi/4) = sin (9*pi + pi/4)

=> sin ( 4*pi + Pi + pi/4)

=> -sin (pi/4)

=> -1/sqrt 2

cos 13pi/6  = sqrt 3/2 and sin 37pi/4 = -1/sqrt 2

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