# Trigonometry Examples

Solve for r 4/3pir^3=36pi
Multiply both sides of the equation by .
Simplify both sides of the equation.
Combine and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
Combine and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Move to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
Move to the left of .
Raise to the power of .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set the factor equal to .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Move to the left of .
Multiply by .
Factor out of .
Multiply by .
Multiply by .
The final answer is the combination of both solutions.
The solution is the result of and .