Trigonometry Examples

Simplify (3(cos(100)+isin(100)))^3
Step 1
Apply the distributive property.
Step 2
Use the Binomial Theorem.
Step 3
Simplify terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Apply the product rule to .
Step 3.1.2
Raise to the power of .
Step 3.1.3
Apply the product rule to .
Step 3.1.4
Multiply by by adding the exponents.
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Step 3.1.4.1
Move .
Step 3.1.4.2
Multiply by .
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Step 3.1.4.2.1
Raise to the power of .
Step 3.1.4.2.2
Use the power rule to combine exponents.
Step 3.1.4.3
Add and .
Step 3.1.5
Multiply by by adding the exponents.
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Step 3.1.5.1
Move .
Step 3.1.5.2
Multiply by .
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Step 3.1.5.2.1
Raise to the power of .
Step 3.1.5.2.2
Use the power rule to combine exponents.
Step 3.1.5.3
Add and .
Step 3.1.6
Raise to the power of .
Step 3.1.7
Multiply by .
Step 3.1.8
Use the power rule to distribute the exponent.
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Step 3.1.8.1
Apply the product rule to .
Step 3.1.8.2
Apply the product rule to .
Step 3.1.9
Raise to the power of .
Step 3.1.10
Rewrite as .
Step 3.1.11
Multiply by .
Step 3.1.12
Multiply by .
Step 3.1.13
Use the power rule to distribute the exponent.
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Step 3.1.13.1
Apply the product rule to .
Step 3.1.13.2
Apply the product rule to .
Step 3.1.14
Raise to the power of .
Step 3.1.15
Factor out .
Step 3.1.16
Rewrite as .
Step 3.1.17
Rewrite as .
Step 3.1.18
Multiply by .
Step 3.2
Simplify the expression.
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Step 3.2.1
Reorder factors in .
Step 3.2.2
Reorder and .