Trigonometry Examples

Solve for ? square root of 3sin(x)=cos(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
Rewrite the expression.
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
Multiply by .
Step 6.3.2
Combine and simplify the denominator.
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Step 6.3.2.1
Multiply by .
Step 6.3.2.2
Raise to the power of .
Step 6.3.2.3
Raise to the power of .
Step 6.3.2.4
Use the power rule to combine exponents.
Step 6.3.2.5
Add and .
Step 6.3.2.6
Rewrite as .
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Step 6.3.2.6.1
Use to rewrite as .
Step 6.3.2.6.2
Apply the power rule and multiply exponents, .
Step 6.3.2.6.3
Combine and .
Step 6.3.2.6.4
Cancel the common factor of .
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Step 6.3.2.6.4.1
Cancel the common factor.
Step 6.3.2.6.4.2
Rewrite the expression.
Step 6.3.2.6.5
Evaluate the exponent.
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 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 10
Simplify .
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Step 10.1
To write as a fraction with a common denominator, multiply by .
Step 10.2
Combine fractions.
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Step 10.2.1
Combine and .
Step 10.2.2
Combine the numerators over the common denominator.
Step 10.3
Simplify the numerator.
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Step 10.3.1
Move to the left of .
Step 10.3.2
Add and .
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
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 13
Consolidate the answers.
, for any integer