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( )

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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( )
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( )

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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