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Trigonometry Examples
Step 1
Step 1.1
Find the point at .
Step 1.1.1
Replace the variable with in the expression.
Step 1.1.2
Simplify the result.
Step 1.1.2.1
Simplify each term.
Step 1.1.2.1.1
Apply the distributive property.
Step 1.1.2.1.2
Cancel the common factor of .
Step 1.1.2.1.2.1
Move the leading negative in into the numerator.
Step 1.1.2.1.2.2
Cancel the common factor.
Step 1.1.2.1.2.3
Rewrite the expression.
Step 1.1.2.1.3
Cancel the common factor of .
Step 1.1.2.1.3.1
Move the leading negative in into the numerator.
Step 1.1.2.1.3.2
Cancel the common factor.
Step 1.1.2.1.3.3
Rewrite the expression.
Step 1.1.2.2
Simplify by adding terms.
Step 1.1.2.2.1
Add and .
Step 1.1.2.2.2
Add and .
Step 1.1.2.3
The exact value of is .
Step 1.1.2.4
Multiply .
Step 1.1.2.4.1
Multiply by .
Step 1.1.2.4.2
Combine and .
Step 1.1.2.5
Move the negative in front of the fraction.
Step 1.1.2.6
The final answer is .
Step 1.2
Find the point at .
Step 1.2.1
Replace the variable with in the expression.
Step 1.2.2
Simplify the result.
Step 1.2.2.1
Simplify each term.
Step 1.2.2.1.1
Cancel the common factor of .
Step 1.2.2.1.1.1
Move the leading negative in into the numerator.
Step 1.2.2.1.1.2
Factor out of .
Step 1.2.2.1.1.3
Cancel the common factor.
Step 1.2.2.1.1.4
Rewrite the expression.
Step 1.2.2.1.2
Move the negative in front of the fraction.
Step 1.2.2.2
To write as a fraction with a common denominator, multiply by .
Step 1.2.2.3
Combine fractions.
Step 1.2.2.3.1
Combine and .
Step 1.2.2.3.2
Combine the numerators over the common denominator.
Step 1.2.2.4
Simplify the numerator.
Step 1.2.2.4.1
Apply the distributive property.
Step 1.2.2.4.2
Multiply by .
Step 1.2.2.4.3
Multiply by .
Step 1.2.2.4.4
Move to the left of .
Step 1.2.2.4.5
Add and .
Step 1.2.2.5
The final answer is .
Step 1.3
Find the point at .
Step 1.3.1
Replace the variable with in the expression.
Step 1.3.2
Simplify the result.
Step 1.3.2.1
Simplify each term.
Step 1.3.2.1.1
Cancel the common factor of .
Step 1.3.2.1.1.1
Move the leading negative in into the numerator.
Step 1.3.2.1.1.2
Factor out of .
Step 1.3.2.1.1.3
Cancel the common factor.
Step 1.3.2.1.1.4
Rewrite the expression.
Step 1.3.2.1.2
Multiply by .
Step 1.3.2.2
Add and .
Step 1.3.2.3
The final answer is .
Step 1.4
Find the point at .
Step 1.4.1
Replace the variable with in the expression.
Step 1.4.2
Simplify the result.
Step 1.4.2.1
Cancel the common factor of .
Step 1.4.2.1.1
Factor out of .
Step 1.4.2.1.2
Cancel the common factor.
Step 1.4.2.1.3
Rewrite the expression.
Step 1.4.2.2
To write as a fraction with a common denominator, multiply by .
Step 1.4.2.3
Combine fractions.
Step 1.4.2.3.1
Combine and .
Step 1.4.2.3.2
Combine the numerators over the common denominator.
Step 1.4.2.4
Simplify the numerator.
Step 1.4.2.4.1
Move to the left of .
Step 1.4.2.4.2
Add and .
Step 1.4.2.5
The final answer is .
Step 1.5
Find the point at .
Step 1.5.1
Replace the variable with in the expression.
Step 1.5.2
Simplify the result.
Step 1.5.2.1
Cancel the common factor of .
Step 1.5.2.1.1
Cancel the common factor.
Step 1.5.2.1.2
Rewrite the expression.
Step 1.5.2.2
Add and .
Step 1.5.2.3
The final answer is .
Step 1.6
List the points in a table.
Step 2
The trig function can be graphed using the points.
Step 3