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Solving Trig Functions: How Do You Solve For Sin 7.5 Using Half-Angle and Double-Angle Identities?

  • trig -

    Formulas to remember:

    sin(2a)=2sin(a)cos(a)
    cos(2a)=cos²(a)-sin²(a)
    From the second equation, replace a by a/2 and 2a by a to get
    cos(a)=cos²(a/2)-sin²(a/2)
    =2cos²(a/2)-1 ...(1)
    =1-2sin²(a/2) ...(2)

    From (1) we get
    cos²(a/2)=(1/2)(1+cos(a))
    From (2) we get
    sin²(a/2)=(1/2)(1-cos(a))

    So
    sin(7.5)
    =√((1/2)(1-cos(15))
    =√((1/2)(1-√((1/2)(1+cos(30))))
    =√((1/2)(1-√((1/2)(1+√(3)/2)))
    =0.13...

  • trig -

    dersagt

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