# Calculus Examples

,

Step 1

Set up the parametric equation for to solve the equation for .

Step 2

Rewrite the equation as .

Step 3

Subtract from both sides of the equation.

Step 4

Step 4.1

Divide each term in by .

Step 4.2

Simplify the left side.

Step 4.2.1

Cancel the common factor of .

Step 4.2.1.1

Cancel the common factor.

Step 4.2.1.2

Divide by .

Step 4.3

Simplify the right side.

Step 4.3.1

Simplify each term.

Step 4.3.1.1

Cancel the common factor of and .

Step 4.3.1.1.1

Factor out of .

Step 4.3.1.1.2

Cancel the common factors.

Step 4.3.1.1.2.1

Factor out of .

Step 4.3.1.1.2.2

Cancel the common factor.

Step 4.3.1.1.2.3

Rewrite the expression.

Step 4.3.1.2

Move the negative in front of the fraction.

Step 5

Replace in the equation for to get the equation in terms of .

Step 6

Step 6.1

Rewrite as .

Step 6.2

Expand using the FOIL Method.

Step 6.2.1

Apply the distributive property.

Step 6.2.2

Apply the distributive property.

Step 6.2.3

Apply the distributive property.

Step 6.3

Simplify and combine like terms.

Step 6.3.1

Simplify each term.

Step 6.3.1.1

Multiply .

Step 6.3.1.1.1

Multiply by .

Step 6.3.1.1.2

Raise to the power of .

Step 6.3.1.1.3

Raise to the power of .

Step 6.3.1.1.4

Use the power rule to combine exponents.

Step 6.3.1.1.5

Add and .

Step 6.3.1.1.6

Multiply by .

Step 6.3.1.2

Multiply .

Step 6.3.1.2.1

Multiply by .

Step 6.3.1.2.2

Multiply by .

Step 6.3.1.3

Multiply .

Step 6.3.1.3.1

Multiply by .

Step 6.3.1.3.2

Multiply by .

Step 6.3.1.4

Multiply .

Step 6.3.1.4.1

Multiply by .

Step 6.3.1.4.2

Multiply by .

Step 6.3.1.4.3

Multiply by .

Step 6.3.1.4.4

Multiply by .

Step 6.3.2

Subtract from .

Step 6.4

Simplify each term.

Step 6.4.1

Cancel the common factor of .

Step 6.4.1.1

Factor out of .

Step 6.4.1.2

Factor out of .

Step 6.4.1.3

Cancel the common factor.

Step 6.4.1.4

Rewrite the expression.

Step 6.4.2

Rewrite as .