Question

高一数学。。。2.3题

Answer 1

cos(-17π/4)=cos(17π/4)=cos(4π+π/4)=cos(π/4)=√2/2；
sin(-1547º)=-sin(1547º)=-sin(4×360º+107º)=-sin107º=-sin(90º+17º)=-cos17º=-09563；
sin(-2160º52')=-sin(2160º52')=-sin(6×360º+52')=-sin52'=-0.01512；
cos(-1751º36')=cos(1751º36')=cos(5×360º-48º24')=cos(48º24')=0.6639；
cos1615º08'=cos(4×360º+175º08')=cos175º08'=cos(180º-4º52')=-cos4º08'=-0.9974；
sin(-26π/3)=-sin(26π/3)=-sin(8π+2π/3)=-sin(2π/3)=-sin(π-π/3)=-sin(π/3)=-√3/2.
3.化简：
(1).sin(-1071º)sin99º+sin(-171º)sin(-261º)=sin(1071º)sin99º+sin171ºsin261º
=sin(3×360º-9º)sin(90º+9º)+sin(180º-9º)sin(270º-9º)
=-sin9ºcos9º-sin9ºcos9º=-2sin9ºcosº=-sin18º
(2)。1+sin(α-2π)sin(π+α)-cos²(-α)=1-sin(2π-α)(-sinα)-cos²α=1+sinα(-sinα)+cos²α
=1-sin²α+cos²α=2cos²α=1+cos2α.