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Trigonometry Examples
Step 1
Divide each term in the equation by .
Step 2
Step 2.1
Cancel the common factor.
Step 2.2
Divide by .
Step 3
Separate fractions.
Step 4
Convert from to .
Step 5
Divide by .
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
Rewrite the expression.
Step 7.2.2
Cancel the common factor of .
Step 7.2.2.1
Cancel the common factor.
Step 7.2.2.2
Divide by .
Step 7.3
Simplify the right side.
Step 7.3.1
Cancel the common factor of .
Step 7.3.1.1
Cancel the common factor.
Step 7.3.1.2
Rewrite the expression.
Step 7.3.2
Multiply by .
Step 7.3.3
Combine and simplify the denominator.
Step 7.3.3.1
Multiply by .
Step 7.3.3.2
Raise to the power of .
Step 7.3.3.3
Raise to the power of .
Step 7.3.3.4
Use the power rule to combine exponents.
Step 7.3.3.5
Add and .
Step 7.3.3.6
Rewrite as .
Step 7.3.3.6.1
Use to rewrite as .
Step 7.3.3.6.2
Apply the power rule and multiply exponents, .
Step 7.3.3.6.3
Combine and .
Step 7.3.3.6.4
Cancel the common factor of .
Step 7.3.3.6.4.1
Cancel the common factor.
Step 7.3.3.6.4.2
Rewrite the expression.
Step 7.3.3.6.5
Evaluate the exponent.
Step 8
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 9
Step 9.1
The exact value of is .
Step 10
The tangent function is positive in the first and third quadrants. To find the second solution, add 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
Move to the left of .
Step 11.3.2
Add and .
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
Step 14
Consolidate the answers.
, for any integer