SAT2数学题The area of the region enclosed by the graph of the p

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：2024/11/10 21:10:33

SAT2数学题
The area of the region enclosed by the graph of the polar curve r=1/(sinx+cosx)and the x- and y-axes is( )

本题要求极坐标下曲线 r=1/(sinx+cosx) 与x轴 y轴围成的区域的面积
首先把极坐标方程转化为直角坐标方程
x=r*cosx
y=r*sinx 这里的r是极距 x是夹角（一般夹角用θ表示）
得cosx=x/r sinx=y/r 带入极坐标方程
r=1/(x/r+y/r) 化简得到直角坐标方程为 x+y=1
也就是直线 y=1-x与两个坐标轴围成的面积很简单了答案是1/2

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