Trigonometry Examples

Convert to Rectangular (1/4*(cos(pi/10)+isin(pi/10)))^5
Step 1
Apply the distributive property.
Step 2
Combine and .
Step 3
Multiply .
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Step 3.1
Combine and .
Step 3.2
Combine and .
Step 4
Use the Binomial Theorem.
Step 5
Simplify terms.
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Step 5.1
Simplify each term.
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Step 5.1.1
Apply the product rule to .
Step 5.1.2
Raise to the power of .
Step 5.1.3
Apply the product rule to .
Step 5.1.4
Raise to the power of .
Step 5.1.5
Combine and .
Step 5.1.6
Combine.
Step 5.1.7
Multiply by .
Step 5.1.8
Apply the product rule to .
Step 5.1.9
Raise to the power of .
Step 5.1.10
Cancel the common factor of .
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Step 5.1.10.1
Factor out of .
Step 5.1.10.2
Factor out of .
Step 5.1.10.3
Cancel the common factor.
Step 5.1.10.4
Rewrite the expression.
Step 5.1.11
Combine and .
Step 5.1.12
Use the power rule to distribute the exponent.
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Step 5.1.12.1
Apply the product rule to .
Step 5.1.12.2
Apply the product rule to .
Step 5.1.13
Combine.
Step 5.1.14
Simplify the numerator.
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Step 5.1.14.1
Rewrite as .
Step 5.1.14.2
Combine exponents.
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Step 5.1.14.2.1
Factor out negative.
Step 5.1.14.2.2
Multiply by .
Step 5.1.15
Simplify the denominator.
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Step 5.1.15.1
Rewrite as .
Step 5.1.15.2
Rewrite as .
Step 5.1.15.3
Multiply the exponents in .
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Step 5.1.15.3.1
Apply the power rule and multiply exponents, .
Step 5.1.15.3.2
Multiply by .
Step 5.1.15.4
Use the power rule to combine exponents.
Step 5.1.15.5
Add and .
Step 5.1.16
Raise to the power of .
Step 5.1.17
Move the negative in front of the fraction.
Step 5.1.18
Apply the product rule to .
Step 5.1.19
Raise to the power of .
Step 5.1.20
Cancel the common factor of .
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Step 5.1.20.1
Factor out of .
Step 5.1.20.2
Factor out of .
Step 5.1.20.3
Cancel the common factor.
Step 5.1.20.4
Rewrite the expression.
Step 5.1.21
Combine and .
Step 5.1.22
Use the power rule to distribute the exponent.
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Step 5.1.22.1
Apply the product rule to .
Step 5.1.22.2
Apply the product rule to .
Step 5.1.23
Combine.
Step 5.1.24
Simplify the numerator.
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Step 5.1.24.1
Factor out .
Step 5.1.24.2
Rewrite as .
Step 5.1.24.3
Rewrite as .
Step 5.1.24.4
Combine exponents.
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Step 5.1.24.4.1
Factor out negative.
Step 5.1.24.4.2
Multiply by .
Step 5.1.25
Simplify the denominator.
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Step 5.1.25.1
Rewrite as .
Step 5.1.25.2
Rewrite as .
Step 5.1.25.3
Multiply the exponents in .
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Step 5.1.25.3.1
Apply the power rule and multiply exponents, .
Step 5.1.25.3.2
Multiply by .
Step 5.1.25.4
Use the power rule to combine exponents.
Step 5.1.25.5
Add and .
Step 5.1.26
Raise to the power of .
Step 5.1.27
Move the negative in front of the fraction.
Step 5.1.28
Combine and .
Step 5.1.29
Use the power rule to distribute the exponent.
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Step 5.1.29.1
Apply the product rule to .
Step 5.1.29.2
Apply the product rule to .
Step 5.1.30
Combine.
Step 5.1.31
Multiply by by adding the exponents.
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Step 5.1.31.1
Multiply by .
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Step 5.1.31.1.1
Raise to the power of .
Step 5.1.31.1.2
Use the power rule to combine exponents.
Step 5.1.31.2
Add and .
Step 5.1.32
Simplify the numerator.
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Step 5.1.32.1
Rewrite as .
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Step 5.1.32.1.1
Rewrite as .
Step 5.1.32.1.2
Rewrite as .
Step 5.1.32.1.3
Raise to the power of .
Step 5.1.32.2
Multiply by .
Step 5.1.33
Raise to the power of .
Step 5.1.34
Use the power rule to distribute the exponent.
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Step 5.1.34.1
Apply the product rule to .
Step 5.1.34.2
Apply the product rule to .
Step 5.1.35
Simplify the numerator.
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Step 5.1.35.1
Factor out .
Step 5.1.35.2
Rewrite as .
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Step 5.1.35.2.1
Rewrite as .
Step 5.1.35.2.2
Rewrite as .
Step 5.1.35.2.3
Raise to the power of .
Step 5.1.35.3
Multiply by .
Step 5.1.36
Raise to the power of .
Step 5.2
Simplify the expression.
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Step 5.2.1
Reorder factors in .
Step 5.2.2
Reorder and .
Step 5.2.3
Reorder and .