trigonometry

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14. Solve sin 2x + sin x = 0 for 0 ≤ x ≤ 2π.

21. Write 2sin37°sin26° as a sum (or difference).

  • trigonometry -

    14.
    sin 2x + sinx = 0
    2sinxcosx + sinx = 0
    sinx(2cosx + 1) = 0
    sinx = 0 or sinx = -1/2

    for sinx = 0
    x = 0, π, 2π

    for sinx = -1/2
    x = 7π/6 or 11π/6 ( 210° or 330°)

    21.
    recall:
    cos u - cosv = -2sin( (u+v)/2 ) sin( (u-v)/2 )

    let (u+v)/2 = 37 ---> u+v = 74
    let (u-v)/2= 26 ----> u-v = 52
    add them:
    2u = 126
    u = 63 , then v = 11

    -2 sin((63+11)/2) sin((63-11)/2) = cos 63 - cos 11
    2 sin((63+11)/2) sin((63-11)/2) = cos11° - cos63°

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