Trigonometry Examples

Solve for x 5tan(x)cos(x)=7cos(x)
Step 1
Simplify the left side.
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Step 1.1
Rewrite in terms of sines and cosines, then cancel the common factors.
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Step 1.1.1
Add parentheses.
Step 1.1.2
Rewrite in terms of sines and cosines.
Step 1.1.3
Cancel the common factors.
Step 2
Divide each term in the equation by .
Step 3
Separate fractions.
Step 4
Convert from to .
Step 5
Divide by .
Step 6
Cancel the common factor of .
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Step 6.1
Cancel the common factor.
Step 6.2
Divide by .
Step 7
Divide each term in by and simplify.
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Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
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Step 7.2.1
Cancel the common factor of .
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Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Divide by .
Step 8
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 9
Simplify the right side.
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Step 9.1
Evaluate .
Step 10
The tangent 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 11
Solve for .
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Step 11.1
Remove parentheses.
Step 11.2
Remove parentheses.
Step 11.3
Add and .
Step 12
Find the period of .
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Step 12.1
The period of the function can be calculated using .
Step 12.2
Replace with in the formula for period.
Step 12.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 12.4
Divide by .
Step 13
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 14
Consolidate and to .
, for any integer