trig

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Find exact value of the expression.
sin( 27pi/4 + 17pi/6)

  • trig -

    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

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