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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
The exact value of is .
Step 1.1.2.2
Subtract full rotations of until the angle is greater than or equal to and less than .
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
The exact value of is .
Step 1.2.2.2
Multiply .
Step 1.2.2.2.1
Combine and .
Step 1.2.2.2.2
Multiply by .
Step 1.2.2.3
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
Step 1.2.2.4
The exact value of is .
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
The exact value of is .
Step 1.3.2.2
Cancel the common factor of .
Step 1.3.2.2.1
Cancel the common factor.
Step 1.3.2.2.2
Rewrite the expression.
Step 1.3.2.3
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 1.3.2.4
The exact value of is .
Step 1.3.2.5
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
The exact value of is .
Step 1.4.2.2
Combine and .
Step 1.4.2.3
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 1.4.2.4
The exact value of is .
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
The exact value of is .
Step 1.5.2.2
Multiply 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