Trigonometry Examples

Solve for c ( square root of 3)/2=34 1/2/c
Step 1
Simplify the right side.
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Step 1.1
Simplify .
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Step 1.1.1
Convert to an improper fraction.
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Step 1.1.1.1
A mixed number is an addition of its whole and fractional parts.
Step 1.1.1.2
Add and .
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Step 1.1.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.1.2.2
Combine and .
Step 1.1.1.2.3
Combine the numerators over the common denominator.
Step 1.1.1.2.4
Simplify the numerator.
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Step 1.1.1.2.4.1
Multiply by .
Step 1.1.1.2.4.2
Add and .
Step 1.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 1.1.3
Multiply by .
Step 2
Rewrite the equation as .
Step 3
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Step 4
Solve the equation for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Multiply by .
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 .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Cancel the common factor of and .
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Step 4.3.3.1.1
Factor out of .
Step 4.3.3.1.2
Cancel the common factors.
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Step 4.3.3.1.2.1
Factor out of .
Step 4.3.3.1.2.2
Cancel the common factor.
Step 4.3.3.1.2.3
Rewrite the expression.
Step 4.3.3.2
Multiply by .
Step 4.3.3.3
Combine and simplify the denominator.
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Step 4.3.3.3.1
Multiply by .
Step 4.3.3.3.2
Raise to the power of .
Step 4.3.3.3.3
Raise to the power of .
Step 4.3.3.3.4
Use the power rule to combine exponents.
Step 4.3.3.3.5
Add and .
Step 4.3.3.3.6
Rewrite as .
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Step 4.3.3.3.6.1
Use to rewrite as .
Step 4.3.3.3.6.2
Apply the power rule and multiply exponents, .
Step 4.3.3.3.6.3
Combine and .
Step 4.3.3.3.6.4
Cancel the common factor of .
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Step 4.3.3.3.6.4.1
Cancel the common factor.
Step 4.3.3.3.6.4.2
Rewrite the expression.
Step 4.3.3.3.6.5
Evaluate the exponent.
Step 4.3.3.4
Cancel the common factor of and .
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Step 4.3.3.4.1
Factor out of .
Step 4.3.3.4.2
Cancel the common factors.
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Step 4.3.3.4.2.1
Factor out of .
Step 4.3.3.4.2.2
Cancel the common factor.
Step 4.3.3.4.2.3
Rewrite the expression.
Step 4.3.3.4.2.4
Divide by .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: