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Trigonometry Examples
Step 1
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 2
Step 2.1
The exact value of is .
Step 3
Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
Step 3.2.1
Cancel the common factor of .
Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 4
The cosine function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Step 5
Step 5.1
Subtract from .
Step 5.2
Divide each term in by and simplify.
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Step 5.2.2.1
Cancel the common factor of .
Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 6
Step 6.1
The period of the function can be calculated using .
Step 6.2
Replace with in the formula for period.
Step 6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.4
Cancel the common factor of and .
Step 6.4.1
Factor out of .
Step 6.4.2
Cancel the common factors.
Step 6.4.2.1
Factor out of .
Step 6.4.2.2
Cancel the common factor.
Step 6.4.2.3
Rewrite the expression.
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer