Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
Solve for θ
Solve for r
θ={arccos(r2)+2kπ−arccos(r2)+2kπ,k∈Z
Evaluate
r2=cos(θ)
Swap the sides of the equation
cos(θ)=r2
Use the inverse trigonometric function
θ=arccos(r2)
Calculate
θ=arccos(r2)θ=−arccos(r2)
Add the period of 2kπ,k∈Z to find all solutions
θ=arccos(r2)+2kπ,k∈Zθ=−arccos(r2)+2kπ,k∈Z
Solution
θ={arccos(r2)+2kπ−arccos(r2)+2kπ,k∈Z
Show Solution
Rewrite the equation
x6+3x4y2+3x2y4+y6=x2
Evaluate
r2=cos(θ)
Multiply both sides
r3=rcos(θ)
Rewrite the expression
−rcos(θ)+r3=0
To covert the equation to rectangular coordinates using conversion formulas,substitute rcosθ for x
−x+r3=0
Simplify the expression
r3=x
Evaluate
r2×r=x
Evaluate
(x2+y2)r=x
Square both sides of the equation
((x2+y2)r)2=x2
Evaluate
(x2+y2)2r2=x2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
(x2+y2)2(x2+y2)=x2
Use substitution
(x2+y2)3=x2
Solution
x6+3x4y2+3x2y4+y6=x2
Show Solution