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Trigonometry Examples
Step 1
Subtract from both sides of the equation.
Step 2
Step 2.1
Move .
Step 2.2
Reorder and .
Step 2.3
Rewrite as .
Step 2.4
Factor out of .
Step 2.5
Factor out of .
Step 2.6
Rewrite as .
Step 2.7
Apply pythagorean identity.
Step 2.8
Add and .
Step 3
Step 3.1
Divide each term in by and simplify.
Step 3.1.1
Divide each term in by .
Step 3.1.2
Simplify the left side.
Step 3.1.2.1
Cancel the common factor of .
Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.1.3
Simplify the right side.
Step 3.1.3.1
Divide by .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Simplify .
Step 3.3.1
Rewrite as .
Step 3.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3.3
Plus or minus is .
Step 3.4
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 3.5
Simplify the right side.
Step 3.5.1
The exact value of is .
Step 3.6
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 3.7
Simplify .
Step 3.7.1
To write as a fraction with a common denominator, multiply by .
Step 3.7.2
Combine fractions.
Step 3.7.2.1
Combine and .
Step 3.7.2.2
Combine the numerators over the common denominator.
Step 3.7.3
Simplify the numerator.
Step 3.7.3.1
Multiply by .
Step 3.7.3.2
Subtract from .
Step 3.8
Find the period of .
Step 3.8.1
The period of the function can be calculated using .
Step 3.8.2
Replace with in the formula for period.
Step 3.8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 3.8.4
Divide by .
Step 3.9
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Step 4
Consolidate the answers.
, for any integer