Trigonometry Examples

Solve for x cot(x)=1/(tan(7/21))
Step 1
Simplify .
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Step 1.1
Cancel the common factor of and .
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Step 1.1.1
Factor out of .
Step 1.1.2
Cancel the common factors.
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Step 1.1.2.1
Factor out of .
Step 1.1.2.2
Cancel the common factor.
Step 1.1.2.3
Rewrite the expression.
Step 1.2
Rewrite in terms of sines and cosines.
Step 1.3
Multiply by the reciprocal of the fraction to divide by .
Step 1.4
Convert from to .
Step 1.5
Evaluate .
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
The cotangent 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 5
Solve for .
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Step 5.1
Remove parentheses.
Step 5.2
Remove parentheses.
Step 5.3
Add and .
Step 6
Find the period of .
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Step 6.1
The period of the function can be calculated using .
Step 6.2
Replace with in the formula for period.
Step 6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.4
Divide by .
Step 7
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 8
Consolidate and to .
, for any integer