Question

sin 165 by compond angle

Answer 1

HeÿA ✒✒

express 165 degrees as an acute angle:

180 - 165 = 15 degrees

Since 165 degrees is in the second quadrant, cos 165 is negative. Hence we have:

cos 165 = - cos 15

Now express 15 degrees as the difference between 60 and 45:

cos 165 = - cos 15 = - cos(60 - 45)

Now use the difference formula:

cos(A - B) = cos(A)cos(B) - sin(A)sin(B)

which gives:

cos 165 = -[cos60*cos45 - sin60*sin45]

= - [1/2 * 1/sqrt(2) - sqrt(3)/2 * 1/sqrt(2)]

= -[1 + sqrt(3) / 2 sqrt(2)

Now rationalise the denominator:

cos 165 = - [ sqrt(2) (1 + sqrt(3)/ 2 sqrt(2)sqrt(2)]

= - [sqrt(2) + sqrt(6)/4]

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