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Trigonometry Examples
Step 1
Step 1.1
Apply the product rule to .
Step 1.2
Rewrite as .
Step 1.2.1
Use to rewrite as .
Step 1.2.2
Apply the power rule and multiply exponents, .
Step 1.2.3
Combine and .
Step 1.2.4
Cancel the common factor of .
Step 1.2.4.1
Cancel the common factor.
Step 1.2.4.2
Rewrite the expression.
Step 1.2.5
Evaluate the exponent.
Step 1.3
Simplify the expression.
Step 1.3.1
Raise to the power of .
Step 1.3.2
Write as a fraction with a common denominator.
Step 1.3.3
Combine the numerators over the common denominator.
Step 1.3.4
Subtract from .
Step 1.4
Rewrite as .
Step 1.5
Simplify the denominator.
Step 1.5.1
Rewrite as .
Step 1.5.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 3
Step 3.1
Evaluate .
Step 4
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 5
Step 5.1
Multiply by .
Step 5.2
Subtract from .
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
Divide by .
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer