Find exact value of the expression.

Question

sin( 27pi/4 + 17pi/6)

Answer 1

sin( 27pi/4 + 17pi/6)
= sin(1215° + 510°) --- sometimes I think better with degrees
= sin(1725°)
= sin(285°) ---- 1725 = 4*360 + 285
= - sin 75°
=- sin(45°+30°)
= - [sin45cos30 + cos45sin30]
= - [ (1/√2)(√3/2) + (1/√2)(1/2)]
= - (√3 + 1)/(2√2)
or after rationalizing ...
= -(√6 + √2)/4