Trigonometry Examples

Solve for x 6sin(x)=-6cos(x)
Step 1
Divide each term in the equation by .
Step 2
Separate fractions.
Step 3
Convert from to .
Step 4
Divide by .
Step 5
Cancel the common factor of .
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Step 5.1
Cancel the common factor.
Step 5.2
Divide by .
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
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Step 6.3.1
Divide by .
Step 7
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 8
Simplify the right side.
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Step 8.1
The exact value of is .
Step 9
The tangent 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 10
Simplify the expression to find the second solution.
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Step 10.1
Add to .
Step 10.2
The resulting angle of is positive and coterminal with .
Step 11
Find the period of .
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Step 11.1
The period of the function can be calculated using .
Step 11.2
Replace with in the formula for period.
Step 11.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 11.4
Divide by .
Step 12
Add to every negative angle to get positive angles.
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Step 12.1
Add to to find the positive angle.
Step 12.2
To write as a fraction with a common denominator, multiply by .
Step 12.3
Combine fractions.
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Step 12.3.1
Combine and .
Step 12.3.2
Combine the numerators over the common denominator.
Step 12.4
Simplify the numerator.
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Step 12.4.1
Move to the left of .
Step 12.4.2
Subtract from .
Step 12.5
List the new angles.
Step 13
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 14
Consolidate the answers.
, for any integer