Find the exact values of the sine cosine and tangent of the

Find the exact values of the sine, cosine, and tangent of the angle. 15 degree sin(15 degree) = cos(15 degree) = tan(15 degree) =

sin 15 degrees

sin 15 = sin ( 45 - 30 )

applying sin (a-b) formula

sin (a-b) = sin a cos b - cos a sin b

sin ( 45 - 30 ) = sin 45 cos 30 - cos 45 sin 30

plugging the values

1/sqrt2 * sqrt3 / 2 - 1/ sqrt 2 * 1/2

sin 15 = sqrt 3 / 2 sqrt 2 - 1 / 2 sqrt 2 = ( sqrt 3 - 1) / (2 sqrt 2) = .2588

b) cos (15) = cos ( 45 - 30)

applying cos (a-b) formula

cos (a-b) = cos a cos b + sin a sin b

cos ( 45-30 ) = cos 45 cos 30 + sin 45 sin 30

1/sqrt 2 * sqrt 3/ 2 + 1/ sqrt 2*1/2 = sqrt 3 / 2 sqrt 2 + 1 / 2 sqrt 2 = ( 1+ sqrt 3) / ( 2sqrt 2) = .9659

c) tan 15 = tan ( 45 - 30)

tan (a-b) = ( tan a - tan b) / ( 1+ tan a tan b)

tan ( 45 - 30) = tan 45 - tan 30 / (1+ tan 45* tan 30 )

1 - 1/sqrt3 / ( 1+ 1/ sqrt 3)

(sqrt 3 -1 ) / sqrt 3 + 1) = .2679