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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 the numerator.
Step 1.2.1.1
Multiply by .
Step 1.2.1.2
Subtract from .
Step 1.2.2
Simplify the denominator.
Step 1.2.2.1
Add and .
Step 1.2.2.2
Subtract from .
Step 1.2.3
Simplify the expression.
Step 1.2.3.1
Multiply by .
Step 1.2.3.2
Move the negative in front of the fraction.
Step 1.2.4
The final answer is .
Step 1.3
The value at is .
Step 2
Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
Step 2.2.1
Simplify the numerator.
Step 2.2.1.1
Multiply by .
Step 2.2.1.2
Subtract from .
Step 2.2.1.3
Rewrite as .
Step 2.2.1.3.1
Factor out of .
Step 2.2.1.3.2
Rewrite as .
Step 2.2.1.4
Pull terms out from under the radical.
Step 2.2.2
Simplify the denominator.
Step 2.2.2.1
Add and .
Step 2.2.2.2
Subtract from .
Step 2.2.3
Reduce the expression by cancelling the common factors.
Step 2.2.3.1
Multiply by .
Step 2.2.3.2
Cancel the common factor of and .
Step 2.2.3.2.1
Factor out of .
Step 2.2.3.2.2
Cancel the common factors.
Step 2.2.3.2.2.1
Factor out of .
Step 2.2.3.2.2.2
Cancel the common factor.
Step 2.2.3.2.2.3
Rewrite the expression.
Step 2.2.3.3
Move the negative in front of the fraction.
Step 2.2.4
The final answer is .
Step 2.3
The value at is .
Step 3
Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
Step 3.2.1
Simplify the numerator.
Step 3.2.1.1
Multiply by .
Step 3.2.1.2
Subtract from .
Step 3.2.2
Simplify the denominator.
Step 3.2.2.1
Add and .
Step 3.2.2.2
Subtract from .
Step 3.2.3
Simplify the expression.
Step 3.2.3.1
Multiply by .
Step 3.2.3.2
Move the negative in front of the fraction.
Step 3.2.4
The final answer is .
Step 3.3
The value at is .
Step 4
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Simplify the numerator.
Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Subtract from .
Step 4.2.2
Simplify the denominator.
Step 4.2.2.1
Add and .
Step 4.2.2.2
Subtract from .
Step 4.2.3
Multiply by .
Step 4.2.4
The final answer is .
Step 4.3
The value at is .
Step 5
Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
Step 5.2.1
Simplify the numerator.
Step 5.2.1.1
Multiply by .
Step 5.2.1.2
Subtract from .
Step 5.2.1.3
Rewrite as .
Step 5.2.1.3.1
Factor out of .
Step 5.2.1.3.2
Rewrite as .
Step 5.2.1.4
Pull terms out from under the radical.
Step 5.2.2
Simplify the denominator.
Step 5.2.2.1
Add and .
Step 5.2.2.2
Subtract from .
Step 5.2.3
Reduce the expression by cancelling the common factors.
Step 5.2.3.1
Multiply by .
Step 5.2.3.2
Cancel the common factor of and .
Step 5.2.3.2.1
Factor out of .
Step 5.2.3.2.2
Cancel the common factors.
Step 5.2.3.2.2.1
Factor out of .
Step 5.2.3.2.2.2
Cancel the common factor.
Step 5.2.3.2.2.3
Rewrite the expression.
Step 5.2.4
The final answer is .
Step 5.3
The value at is .
Step 6
Step 6.1
Replace the variable with in the expression.
Step 6.2
Simplify the result.
Step 6.2.1
Simplify the numerator.
Step 6.2.1.1
Multiply by .
Step 6.2.1.2
Subtract from .
Step 6.2.2
Simplify the denominator.
Step 6.2.2.1
Add and .
Step 6.2.2.2
Subtract from .
Step 6.2.3
Multiply by .
Step 6.2.4
The final answer is .
Step 6.3
The value at is .
Step 7
List the points to graph.
Step 8
Select a few points to graph.
Step 9