Question
Solve the equation
Solve for θ
Solve for r
θ=2arccos(31r2)
Evaluate
r2=3cos(2θ)
Swap the sides of the equation
3cos(2θ)=r2
Multiply both sides of the equation by 31
3cos(2θ)×31=r2×31
Calculate
cos(2θ)=r2×31
Calculate
cos(2θ)=31r2
Use the inverse trigonometric function
2θ=arccos(31r2)
Divide both sides
22θ=2arccos(31r2)
Solution
θ=2arccos(31r2)
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Rewrite the equation
−3x2+3y2+x4+2x2y2+y4=0
Evaluate
r2=3cos(2θ)
Simplify the expression
r2=3cos2(θ)−3sin2(θ)
Multiply both sides
r4=3(rcos(θ))2−3(rsin(θ))2
Rewrite the expression
−3(rcos(θ))2+3(rsin(θ))2+r4=0
Solution
More Steps

Evaluate
−3(rcos(θ))2+3(rsin(θ))2+r4
To covert the equation to rectangular coordinates using conversion formulas,substitute rcosθ for x
−3x2+3(rsin(θ))2+r4
To covert the equation to rectangular coordinates using conversion formulas,substitute rsinθ for y
−3x2+3y2+r4
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
−3x2+3y2+(x2+y2)2
Simplify the expression
−3x2+3y2+x4+2x2y2+y4
−3x2+3y2+x4+2x2y2+y4=0
Show Solution
