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Trigonometry Examples
Step 1
Step 1.1
Rewrite in terms of sines and cosines, then cancel the common factors.
Step 1.1.1
Rewrite in terms of sines and cosines.
Step 1.1.2
Cancel the common factors.
Step 2
Step 2.1
Simplify .
Step 2.1.1
Rewrite in terms of sines and cosines.
Step 2.1.2
Combine and .
Step 3
Multiply both sides of the equation by .
Step 4
Step 4.1
Cancel the common factor.
Step 4.2
Rewrite the expression.
Step 5
Step 5.1
Cancel the common factor.
Step 5.2
Rewrite the expression.
Step 6
Rewrite the equation as .
Step 7
Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
Step 7.2.1
Cancel the common factor of .
Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Divide by .
Step 8
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 9
Step 9.1
The exact value of is .
Step 10
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 11
Step 11.1
To write as a fraction with a common denominator, multiply by .
Step 11.2
Combine fractions.
Step 11.2.1
Combine and .
Step 11.2.2
Combine the numerators over the common denominator.
Step 11.3
Simplify the numerator.
Step 11.3.1
Multiply by .
Step 11.3.2
Subtract from .
Step 12
Step 12.1
The period of the function can be calculated using .
Step 12.2
Replace with in the formula for period.
Step 12.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 12.4
Divide by .
Step 13
The period of the function is so values will repeat every radians in both directions.
, for any integer