Precalculus Examples

Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Step 3
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 4
Simplify the right side.
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The exact value of is .
Step 5
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Step 6
Simplify .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Step 7
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Step 8
The period of the function is so values will repeat every radians in both directions.
, for any integer
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