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Trigonometry Examples
Step 1
Step 1.1
Replace the variable with in the expression.
Step 1.2
Simplify the result.
Step 1.2.1
Simplify each term.
Step 1.2.1.1
Raise to the power of .
Step 1.2.1.2
Divide by .
Step 1.2.1.3
Multiply by .
Step 1.2.1.4
Raise to the power of .
Step 1.2.1.5
Multiply by .
Step 1.2.1.6
Multiply by .
Step 1.2.2
Simplify by adding and subtracting.
Step 1.2.2.1
Subtract from .
Step 1.2.2.2
Subtract from .
Step 1.2.2.3
Add and .
Step 1.2.3
The final answer is .
Step 1.3
Convert to decimal.
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Cancel the common factor of and .
Step 2.2.1.1.1
Rewrite as .
Step 2.2.1.1.2
Apply the product rule to .
Step 2.2.1.1.3
Raise to the power of .
Step 2.2.1.1.4
Factor out of .
Step 2.2.1.1.5
Cancel the common factors.
Step 2.2.1.1.5.1
Factor out of .
Step 2.2.1.1.5.2
Cancel the common factor.
Step 2.2.1.1.5.3
Rewrite the expression.
Step 2.2.1.1.5.4
Divide by .
Step 2.2.1.2
Rewrite as .
Step 2.2.1.3
Raise to the power of .
Step 2.2.1.4
Multiply .
Step 2.2.1.4.1
Multiply by .
Step 2.2.1.4.2
Multiply by .
Step 2.2.1.5
Raise to the power of .
Step 2.2.1.6
Multiply by .
Step 2.2.1.7
Multiply by .
Step 2.2.2
Simplify by adding and subtracting.
Step 2.2.2.1
Subtract from .
Step 2.2.2.2
Subtract from .
Step 2.2.2.3
Add and .
Step 2.2.3
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Raise to the power of .
Step 3.2.1.2
Move the negative in front of the fraction.
Step 3.2.1.3
Multiply .
Step 3.2.1.3.1
Multiply by .
Step 3.2.1.3.2
Multiply by .
Step 3.2.1.4
Raise to the power of .
Step 3.2.1.5
Multiply by .
Step 3.2.1.6
Multiply by .
Step 3.2.2
Find the common denominator.
Step 3.2.2.1
Write as a fraction with denominator .
Step 3.2.2.2
Multiply by .
Step 3.2.2.3
Multiply by .
Step 3.2.2.4
Write as a fraction with denominator .
Step 3.2.2.5
Multiply by .
Step 3.2.2.6
Multiply by .
Step 3.2.2.7
Write as a fraction with denominator .
Step 3.2.2.8
Multiply by .
Step 3.2.2.9
Multiply by .
Step 3.2.3
Combine the numerators over the common denominator.
Step 3.2.4
Simplify each term.
Step 3.2.4.1
Multiply by .
Step 3.2.4.2
Multiply by .
Step 3.2.4.3
Multiply by .
Step 3.2.5
Simplify the expression.
Step 3.2.5.1
Subtract from .
Step 3.2.5.2
Subtract from .
Step 3.2.5.3
Add and .
Step 3.2.5.4
Move the negative in front of the fraction.
Step 3.2.6
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Simplify each term.
Step 4.2.1.1
Raise to the power of .
Step 4.2.1.2
Move the negative in front of the fraction.
Step 4.2.1.3
Multiply .
Step 4.2.1.3.1
Multiply by .
Step 4.2.1.3.2
Multiply by .
Step 4.2.1.4
Multiply by by adding the exponents.
Step 4.2.1.4.1
Multiply by .
Step 4.2.1.4.1.1
Raise to the power of .
Step 4.2.1.4.1.2
Use the power rule to combine exponents.
Step 4.2.1.4.2
Add and .
Step 4.2.1.5
Raise to the power of .
Step 4.2.1.6
Multiply by .
Step 4.2.2
Find the common denominator.
Step 4.2.2.1
Write as a fraction with denominator .
Step 4.2.2.2
Multiply by .
Step 4.2.2.3
Multiply by .
Step 4.2.2.4
Write as a fraction with denominator .
Step 4.2.2.5
Multiply by .
Step 4.2.2.6
Multiply by .
Step 4.2.2.7
Write as a fraction with denominator .
Step 4.2.2.8
Multiply by .
Step 4.2.2.9
Multiply by .
Step 4.2.3
Combine the numerators over the common denominator.
Step 4.2.4
Simplify each term.
Step 4.2.4.1
Multiply by .
Step 4.2.4.2
Multiply by .
Step 4.2.4.3
Multiply by .
Step 4.2.5
Simplify the expression.
Step 4.2.5.1
Subtract from .
Step 4.2.5.2
Subtract from .
Step 4.2.5.3
Add and .
Step 4.2.5.4
Move the negative in front of the fraction.
Step 4.2.6
The final answer is .
Step 4.3
Convert to decimal.
Step 5
Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
Step 5.2.1
Simplify each term.
Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Move the negative in front of the fraction.
Step 5.2.1.3
Multiply .
Step 5.2.1.3.1
Multiply by .
Step 5.2.1.3.2
Multiply by .
Step 5.2.1.4
Raise to the power of .
Step 5.2.1.5
Multiply by .
Step 5.2.1.6
Multiply by .
Step 5.2.2
Find the common denominator.
Step 5.2.2.1
Write as a fraction with denominator .
Step 5.2.2.2
Multiply by .
Step 5.2.2.3
Multiply by .
Step 5.2.2.4
Write as a fraction with denominator .
Step 5.2.2.5
Multiply by .
Step 5.2.2.6
Multiply by .
Step 5.2.2.7
Write as a fraction with denominator .
Step 5.2.2.8
Multiply by .
Step 5.2.2.9
Multiply by .
Step 5.2.3
Combine the numerators over the common denominator.
Step 5.2.4
Simplify each term.
Step 5.2.4.1
Multiply by .
Step 5.2.4.2
Multiply by .
Step 5.2.4.3
Multiply by .
Step 5.2.5
Simplify by adding and subtracting.
Step 5.2.5.1
Subtract from .
Step 5.2.5.2
Subtract from .
Step 5.2.5.3
Add and .
Step 5.2.6
The final answer is .
Step 5.3
Convert to decimal.
Step 6
The cubic function can be graphed using the function behavior and the points.
Step 7
The cubic function can be graphed using the function behavior and the selected points.
Rises to the left and falls to the right
Step 8