Question
Function
Find the inverse
Evaluate the derivative
Find the domain
Load more

f−1(θ)=2arcsin(892θ)
Evaluate
r=−89cos(θ)sin(θ)
Simplify
r=−289sin(2θ)
Interchange θ and y
θ=−289sin(2y)
Calculate
More Steps

Evaluate
θ=−289sin(2y)
Swap the sides of the equation
−289sin(2y)=θ
Multiply both sides of the equation by 892
−289sin(2y)×892=θ×892
Calculate
sin(2y)=θ×892
Calculate
sin(2y)=892θ
Use the inverse trigonometric function
2y=arcsin(892θ)
Divide both sides
22y=2arcsin(892θ)
Divide the numbers
y=2arcsin(892θ)
y=2arcsin(892θ)
Solution
f−1(θ)=2arcsin(892θ)
Show Solution

Solve the equation
Solve for θ
Solve for r
θ=2arcsin(892r)
Evaluate
r=−89cos(θ)sin(θ)
Simplify
r=−289sin(2θ)
Swap the sides of the equation
−289sin(2θ)=r
Multiply both sides of the equation by 892
−289sin(2θ)×892=r×892
Calculate
sin(2θ)=r×892
Calculate
sin(2θ)=892r
Use the inverse trigonometric function
2θ=arcsin(892r)
Divide both sides
22θ=2arcsin(892r)
Solution
θ=2arcsin(892r)
Show Solution

Rewrite the equation
x6+3x4y2+3x2y4+y6=7921y2x2
Evaluate
r=−89cos(θ)sin(θ)
Simplify
r=−289sin(2θ)
Simplify the expression
r=−89sin(θ)cos(θ)
Multiply both sides
r3=−89sin(θ)cos(θ)×r2
Rewrite the expression
89sin(θ)cos(θ)×r2+r3=0
Use substitution
More Steps

Evaluate
89sin(θ)cos(θ)×r2+r3
Use substitution
More Steps

Evaluate
89sin(θ)cos(θ)×r2
Use the commutative property to reorder the terms
r2sin(θ)cos(θ)×89
To covert the equation to rectangular coordinates using conversion formulas,substitute rsinθ for y
rcos(θ)×y×89
To covert the equation to rectangular coordinates using conversion formulas,substitute rcosθ for x
yx×89
Multiply the terms
89yx
89yx+r3
89yx+r3=0
Simplify the expression
r3=−89yx
Evaluate
r2×r=−89yx
Evaluate
(x2+y2)r=−89yx
Square both sides of the equation
((x2+y2)r)2=(−89yx)2
Evaluate
(x2+y2)2r2=(−89yx)2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
(x2+y2)2(x2+y2)=(−89yx)2
Use substitution
(x2+y2)3=(−89yx)2
Evaluate the power
(x2+y2)3=7921y2x2
Solution
x6+3x4y2+3x2y4+y6=7921y2x2
Show Solution
