神马作文网三角函数 (2 21:19:19)
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/12 08:06:33
三角函数 (2 21:19:19)
设f(x)=cosX/cos(30-X),则f(1°)+f(2°)+.+f(59°)=
设f(x)=cosX/cos(30-X),则f(1°)+f(2°)+.+f(59°)=
f(x)+f(60°-x)
=cosx/cos(30-x)+cos(60-x)/cos[30-(60-x)]
=cosx/cos(30-x)+cos(60-x)/cos[x-30]
=[cosx+cos(60-x)]/cos(30-x)
=[cosx+cos60*cosx+sin60*sinx]/(cos30*cosx+sin30*sinx)
=[(3/2)cosx+(√3/2)sinx]/[(√3/2)cosx+(1/2)sinx]
=√3
f(1°)+f(2°)+.+f(59°)
=f(1°)+f(59°)+f(2°)+f(58°)+.+f(29°)+f(31°)+2f(30°)-f(30°)
=30*√3-√3/2
=30√3-√3/2
=59√3/2
=cosx/cos(30-x)+cos(60-x)/cos[30-(60-x)]
=cosx/cos(30-x)+cos(60-x)/cos[x-30]
=[cosx+cos(60-x)]/cos(30-x)
=[cosx+cos60*cosx+sin60*sinx]/(cos30*cosx+sin30*sinx)
=[(3/2)cosx+(√3/2)sinx]/[(√3/2)cosx+(1/2)sinx]
=√3
f(1°)+f(2°)+.+f(59°)
=f(1°)+f(59°)+f(2°)+f(58°)+.+f(29°)+f(31°)+2f(30°)-f(30°)
=30*√3-√3/2
=30√3-√3/2
=59√3/2