Trigonometry Examples

Solve for a r=1/2* square root of a/p
Step 1
Rewrite the equation as .
Step 2
Multiply both sides of the equation by .
Step 3
Simplify the left side.
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Step 3.1
Simplify .
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Step 3.1.1
Rewrite as .
Step 3.1.2
Multiply by .
Step 3.1.3
Combine and simplify the denominator.
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Step 3.1.3.1
Multiply by .
Step 3.1.3.2
Raise to the power of .
Step 3.1.3.3
Raise to the power of .
Step 3.1.3.4
Use the power rule to combine exponents.
Step 3.1.3.5
Add and .
Step 3.1.3.6
Rewrite as .
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Step 3.1.3.6.1
Use to rewrite as .
Step 3.1.3.6.2
Apply the power rule and multiply exponents, .
Step 3.1.3.6.3
Combine and .
Step 3.1.3.6.4
Cancel the common factor of .
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Step 3.1.3.6.4.1
Cancel the common factor.
Step 3.1.3.6.4.2
Rewrite the expression.
Step 3.1.3.6.5
Simplify.
Step 3.1.4
Combine using the product rule for radicals.
Step 3.1.5
Multiply by .
Step 3.1.6
Cancel the common factor of .
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Step 3.1.6.1
Factor out of .
Step 3.1.6.2
Cancel the common factor.
Step 3.1.6.3
Rewrite the expression.
Step 4
Cross multiply.
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Step 4.1
Cross multiply by setting the product of the numerator of the right side and the denominator of the left side equal to the product of the numerator of the left side and the denominator of the right side.
Step 4.2
Simplify the left side.
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Step 4.2.1
Multiply by .
Step 5
Rewrite the equation as .
Step 6
To remove the radical on the left side of the equation, square both sides of the equation.
Step 7
Simplify each side of the equation.
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Step 7.1
Use to rewrite as .
Step 7.2
Simplify the left side.
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Step 7.2.1
Simplify .
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Step 7.2.1.1
Multiply the exponents in .
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Step 7.2.1.1.1
Apply the power rule and multiply exponents, .
Step 7.2.1.1.2
Cancel the common factor of .
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Step 7.2.1.1.2.1
Cancel the common factor.
Step 7.2.1.1.2.2
Rewrite the expression.
Step 7.2.1.2
Simplify.
Step 7.3
Simplify the right side.
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Step 7.3.1
Simplify .
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Step 7.3.1.1
Use the power rule to distribute the exponent.
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Step 7.3.1.1.1
Apply the product rule to .
Step 7.3.1.1.2
Apply the product rule to .
Step 7.3.1.2
Raise to the power of .
Step 8
Divide each term in by and simplify.
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Step 8.1
Divide each term in by .
Step 8.2
Simplify the left side.
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Step 8.2.1
Cancel the common factor of .
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Step 8.2.1.1
Cancel the common factor.
Step 8.2.1.2
Divide by .
Step 8.3
Simplify the right side.
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Step 8.3.1
Cancel the common factor of and .
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Step 8.3.1.1
Factor out of .
Step 8.3.1.2
Cancel the common factors.
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Step 8.3.1.2.1
Raise to the power of .
Step 8.3.1.2.2
Factor out of .
Step 8.3.1.2.3
Cancel the common factor.
Step 8.3.1.2.4
Rewrite the expression.
Step 8.3.1.2.5
Divide by .