Finite Math Examples

Simplify (5(cos(15)+isin(15)))^3
Step 1
Simplify each term.
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Step 1.1
The exact value of is .
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Step 1.1.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.1.2
Separate negation.
Step 1.1.3
Apply the difference of angles identity .
Step 1.1.4
The exact value of is .
Step 1.1.5
The exact value of is .
Step 1.1.6
The exact value of is .
Step 1.1.7
The exact value of is .
Step 1.1.8
Simplify .
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Step 1.1.8.1
Simplify each term.
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Step 1.1.8.1.1
Multiply .
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Step 1.1.8.1.1.1
Multiply by .
Step 1.1.8.1.1.2
Combine using the product rule for radicals.
Step 1.1.8.1.1.3
Multiply by .
Step 1.1.8.1.1.4
Multiply by .
Step 1.1.8.1.2
Multiply .
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Step 1.1.8.1.2.1
Multiply by .
Step 1.1.8.1.2.2
Multiply by .
Step 1.1.8.2
Combine the numerators over the common denominator.
Step 1.2
The exact value of is .
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Step 1.2.1
Split into two angles where the values of the six trigonometric functions are known.
Step 1.2.2
Separate negation.
Step 1.2.3
Apply the difference of angles identity.
Step 1.2.4
The exact value of is .
Step 1.2.5
The exact value of is .
Step 1.2.6
The exact value of is .
Step 1.2.7
The exact value of is .
Step 1.2.8
Simplify .
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Step 1.2.8.1
Simplify each term.
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Step 1.2.8.1.1
Multiply .
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Step 1.2.8.1.1.1
Multiply by .
Step 1.2.8.1.1.2
Combine using the product rule for radicals.
Step 1.2.8.1.1.3
Multiply by .
Step 1.2.8.1.1.4
Multiply by .
Step 1.2.8.1.2
Multiply .
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Step 1.2.8.1.2.1
Multiply by .
Step 1.2.8.1.2.2
Multiply by .
Step 1.2.8.2
Combine the numerators over the common denominator.
Step 1.3
Combine and .
Step 2
Combine fractions.
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Step 2.1
Combine the numerators over the common denominator.
Step 2.2
Combine and .
Step 3
Use the power rule to distribute the exponent.
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Step 3.1
Apply the product rule to .
Step 3.2
Apply the product rule to .
Step 4
Raise to the power of .
Step 5
Raise to the power of .