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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 the numerator.
Step 1.1.2.1.1
Multiply by .
Step 1.1.2.1.2
Combine and .
Step 1.1.2.2
Simplify the expression.
Step 1.1.2.2.1
Multiply by .
Step 1.1.2.2.2
Divide by .
Step 1.1.2.2.3
Divide by .
Step 1.1.2.3
The exact value of is .
Step 1.1.2.4
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 the numerator.
Step 1.2.2.1.1
Multiply by .
Step 1.2.2.1.2
Combine and .
Step 1.2.2.2
Multiply by .
Step 1.2.2.3
Reduce the expression by cancelling the common factors.
Step 1.2.2.3.1
Cancel the common factor of and .
Step 1.2.2.3.1.1
Factor out of .
Step 1.2.2.3.1.2
Cancel the common factors.
Step 1.2.2.3.1.2.1
Factor out of .
Step 1.2.2.3.1.2.2
Cancel the common factor.
Step 1.2.2.3.1.2.3
Rewrite the expression.
Step 1.2.2.3.2
Move the negative in front of the fraction.
Step 1.2.2.4
Multiply the numerator by the reciprocal of the denominator.
Step 1.2.2.5
Cancel the common factor of .
Step 1.2.2.5.1
Move the leading negative in into the numerator.
Step 1.2.2.5.2
Factor out of .
Step 1.2.2.5.3
Cancel the common factor.
Step 1.2.2.5.4
Rewrite the expression.
Step 1.2.2.6
Move the negative in front of the fraction.
Step 1.2.2.7
The exact value of is .
Step 1.2.2.8
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
Cancel the common factor of and .
Step 1.3.2.1.1
Factor out of .
Step 1.3.2.1.2
Cancel the common factors.
Step 1.3.2.1.2.1
Factor out of .
Step 1.3.2.1.2.2
Cancel the common factor.
Step 1.3.2.1.2.3
Rewrite the expression.
Step 1.3.2.1.2.4
Divide by .
Step 1.3.2.2
Multiply by .
Step 1.3.2.3
The exact value of is .
Step 1.3.2.4
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
Combine and .
Step 1.4.2.2
Multiply by .
Step 1.4.2.3
Cancel the common factor of and .
Step 1.4.2.3.1
Factor out of .
Step 1.4.2.3.2
Cancel the common factors.
Step 1.4.2.3.2.1
Factor out of .
Step 1.4.2.3.2.2
Cancel the common factor.
Step 1.4.2.3.2.3
Rewrite the expression.
Step 1.4.2.4
Multiply the numerator by the reciprocal of the denominator.
Step 1.4.2.5
Cancel the common factor of .
Step 1.4.2.5.1
Cancel the common factor.
Step 1.4.2.5.2
Rewrite the expression.
Step 1.4.2.6
The exact value of is .
Step 1.4.2.7
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
Combine and .
Step 1.5.2.2
Simplify the expression.
Step 1.5.2.2.1
Multiply by .
Step 1.5.2.2.2
Divide by .
Step 1.5.2.2.3
Divide by .
Step 1.5.2.3
The exact value of is .
Step 1.5.2.4
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