Trigonometry Examples

Solve for x 6cot(x+5)=-1
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
Move the negative in front of the fraction.
Step 2
Take the inverse cotangent of both sides of the equation to extract from inside the cotangent.
Step 3
Simplify the right side.
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Step 3.1
Evaluate .
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from .
Step 5
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 6
Simplify the expression to find the second solution.
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Step 6.1
Add to .
Step 6.2
The resulting angle of is positive and coterminal with .
Step 6.3
Move all terms not containing to the right side of the equation.
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Step 6.3.1
Subtract from both sides of the equation.
Step 6.3.2
Subtract from .
Step 7
Find the period of .
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Step 7.1
The period of the function can be calculated using .
Step 7.2
Replace with in the formula for period.
Step 7.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 7.4
Divide by .
Step 8
Add to every negative angle to get positive angles.
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Step 8.1
Add to to find the positive angle.
Step 8.2
Replace with decimal approximation.
Step 8.3
Subtract from .
Step 8.4
Add to to find the positive angle.
Step 8.5
Replace with decimal approximation.
Step 8.6
Subtract from .
Step 8.7
List the new angles.
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer