三角函数15 16

1个回答

  • 15已知α为锐角,cos(α+π/6)=4/5,求sin(2α+π/12)

    解析:∵α为锐角,cos(α+π/6)=4/5

    ∴cos^2(α+π/6)=16/25==>1+ cos(2α+π/3)=32/25==>cos(2α+π/3)=7/25

    ∴sin(2α+π/3)=24/25

    sin(2α+π/12)=Sin(2α+π/3-π/4)=Sin(2α+π/3)cosπ/4-cos(2α+π/3)sinπ/4

    =24/25*√2/2-7/25*√2/2=17√2/50

    16已知6sin^2α+sinαcosα-2cos^2α=0,α∈[π/2,π],求sin(2α+π/3)

    解析:6(sina)^2+sina*cosa-2(cosa)^2=0

    (3sina+2cosa)(2sina-cosa)=0

    3sina+2cosa=0或2sina-cosa=0

    tana=-2/3或tana=1/2

    ∵α∈[π/2,π)

    ∴tana