Graph tan(theta)<0

Math
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
The exact value of is .
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.
Add and .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
Find the domain of .
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Set the argument in equal to to find where the expression is undefined.
, for any integer
The domain is all values of that make the expression defined.
, for any integer
, for any integer
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not less than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
True
The solution consists of all of the true intervals.
, for any integer
Graph tan(theta)<0

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