Question

把极坐标方程ρcos2θ=2cos(2π/3-θ)化为直角方程 在线等

Answer 1

两边同乘以ρ
得ρ²cos2θ=2ρcos(2π/3-θ)
用三角带盯公式蠢悔和展开
ρ²(cos²θ-sin²θ)=2ρ(-1/2cosθ+√3/2sinθ)
即ρ²cos²θ-ρ²sin²θ=-ρcosθ+√前搏3ρsinθ
所以x²-y²=-x+√3y

Answer 2

x=ρcosθ
y=ρsinθ

左边=2ρ cosθ sinθ
右边 = 2(cos2π/3 cosθ + sin2π/3 sinθ)
=2(-1/2 cosθ + (根号3)/2 sinθ)
两边同慧帆孙时乘以ρ
2 ρcosθ ρsinθ = 2ρ (-1/2 cosθ + (根号3)/轿胡2 sinθ)
2xy = 2 (-1/2 x+ (根前链号3)/2 y)
xy = (-1/2) x+ [(根号3)/2] y

Answer 3

ρ²(cos²θ－sin²θ)=ρ(－cosθ＋√3sinθ)
x²－y²=－x＋袜喊√芦腔3y。陪好衫

Answer 4

X^2 - Y^2 = -X + √3Y