Trigonometry Examples

Solve for ? cot(x)=2cos(x)
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
Rewrite the expression.
Step 1.3
Simplify the right side.
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Step 1.3.1
Separate fractions.
Step 1.3.2
Rewrite in terms of sines and cosines.
Step 1.3.3
Multiply by the reciprocal of the fraction to divide by .
Step 1.3.4
Write as a fraction with denominator .
Step 1.3.5
Cancel the common factor of .
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Step 1.3.5.1
Cancel the common factor.
Step 1.3.5.2
Rewrite the expression.
Step 1.3.6
Divide by .
Step 2
Rewrite the equation as .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 4
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 5
Simplify the right side.
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Step 5.1
The exact value of is .
Step 6
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Step 7
Simplify .
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Step 7.1
To write as a fraction with a common denominator, multiply by .
Step 7.2
Combine fractions.
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Step 7.2.1
Combine and .
Step 7.2.2
Combine the numerators over the common denominator.
Step 7.3
Simplify the numerator.
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Step 7.3.1
Move to the left of .
Step 7.3.2
Subtract from .
Step 8
Find the period of .
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Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Divide by .
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer