Trigonometry Examples

Solve for l t=2p square root of l/g
Step 1
Rewrite the equation as .
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Simplify each side of the equation.
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Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Apply the product rule to .
Step 3.2.1.2
Multiply .
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Step 3.2.1.2.1
Combine and .
Step 3.2.1.2.2
Combine and .
Step 3.2.1.3
Move to the left of .
Step 3.2.1.4
Use the power rule to distribute the exponent.
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Step 3.2.1.4.1
Apply the product rule to .
Step 3.2.1.4.2
Apply the product rule to .
Step 3.2.1.4.3
Apply the product rule to .
Step 3.2.1.5
Simplify the numerator.
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Step 3.2.1.5.1
Raise to the power of .
Step 3.2.1.5.2
Multiply the exponents in .
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Step 3.2.1.5.2.1
Apply the power rule and multiply exponents, .
Step 3.2.1.5.2.2
Cancel the common factor of .
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Step 3.2.1.5.2.2.1
Cancel the common factor.
Step 3.2.1.5.2.2.2
Rewrite the expression.
Step 3.2.1.5.3
Simplify.
Step 3.2.1.6
Simplify the denominator.
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Step 3.2.1.6.1
Multiply the exponents in .
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Step 3.2.1.6.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.6.1.2
Cancel the common factor of .
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Step 3.2.1.6.1.2.1
Cancel the common factor.
Step 3.2.1.6.1.2.2
Rewrite the expression.
Step 3.2.1.6.2
Simplify.
Step 4
Solve for .
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Step 4.1
Multiply both sides by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Rewrite the expression.
Step 4.3
Divide each term in by and simplify.
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Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Rewrite the expression.
Step 4.3.2.2
Cancel the common factor of .
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Step 4.3.2.2.1
Cancel the common factor.
Step 4.3.2.2.2
Divide by .