Precalculus Examples

Solve for ? cot(x)=- square root of 3
Step 1
Take the inverse cotangent of both sides of the equation to extract from inside the cotangent.
Step 2
Simplify the right side.
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Step 2.1
The exact value of is .
Step 3
The cotangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Step 4
Simplify the expression to find the second solution.
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Step 4.1
Add to .
Step 4.2
The resulting angle of is positive and coterminal with .
Step 5
Find the period of .
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Step 5.1
The period of the function can be calculated using .
Step 5.2
Replace with in the formula for period.
Step 5.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 5.4
Divide by .
Step 6
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 7
Consolidate the answers.
, for any integer