Trigonometry Examples

Solve for m sin((pi/6)/2)=1/m
Step 1
Rewrite the equation as .
Step 2
Simplify both sides.
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Step 2.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.2
Multiply .
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Step 2.2.1
Multiply by .
Step 2.2.2
Multiply by .
Step 2.3
The exact value of is .
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Step 2.3.1
Split into two angles where the values of the six trigonometric functions are known.
Step 2.3.2
Apply the difference of angles identity.
Step 2.3.3
The exact value of is .
Step 2.3.4
The exact value of is .
Step 2.3.5
The exact value of is .
Step 2.3.6
The exact value of is .
Step 2.3.7
Simplify .
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Step 2.3.7.1
Simplify each term.
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Step 2.3.7.1.1
Multiply .
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Step 2.3.7.1.1.1
Multiply by .
Step 2.3.7.1.1.2
Combine using the product rule for radicals.
Step 2.3.7.1.1.3
Multiply by .
Step 2.3.7.1.1.4
Multiply by .
Step 2.3.7.1.2
Multiply .
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Step 2.3.7.1.2.1
Multiply by .
Step 2.3.7.1.2.2
Multiply by .
Step 2.3.7.2
Combine the numerators over the common denominator.
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
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Multiply by .
Step 4.3.3.3
Expand the denominator using the FOIL method.
Step 4.3.3.4
Simplify.
Step 4.3.3.5
Cancel the common factor of .
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Step 4.3.3.5.1
Cancel the common factor.
Step 4.3.3.5.2
Divide by .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: