Trigonometry Examples
Step 3
Cancel the common factor of .
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Step 3.1
Cancel the common factor.
Step 3.2
Step 4
Take the inverse tangent of both sides of the equation to tướng extract from inside the tangent.
Step 5
Simplify the right side.
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Step 6
Divide each term in by and simplify.
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Step 6.1
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Step 6.3
Simplify the right side.
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Step 6.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 6.3.2
Multiply .
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Step 7
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to tướng find the solution in the fourth quadrant.
Step 8
Solve for .
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Step 8.1
Simplify.
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Step 8.1.1
To write as a fraction with a common denominator, multiply by .
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Step 8.1.2
Step 8.1.3
Combine the numerators over the common denominator.
Step 8.1.4
Add and .
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Step 8.2
Divide each term in by and simplify.
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Step 8.2.1
Step 8.2.2
Simplify the left side.
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Step 8.2.2.1
Cancel the common factor of .
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Step 8.2.2.1.1
Cancel the common factor.
Step 8.2.2.1.2
Step 8.2.3
Simplify the right side.
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Step 8.2.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 8.2.3.2
Multiply .
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Step 8.2.3.2.1
Step 8.2.3.2.2
Step 9
Find the period of .
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Step 9.1
The period of the function can be calculated using .
Step 9.2
Replace with in the formula for period.
Step 9.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 10
The period of the function is sánh values will repeat every radians in both directions.
, for any integer
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Step 11
Consolidate the answers.
, for any integer
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