Trigonometry Examples

Find the Equation Given the Roots 3 , 125i
,
Step 1
Roots are the points where the graph intercepts with the x-axis .
at the roots
Step 2
The root at was found by solving for when and .
The factor is
Step 3
The root at was found by solving for when and .
The factor is
Step 4
The root at was found by solving for when and .
The factor is
Step 5
Combine all the factors into a single equation.
Step 6
Multiply all the factors to simplify the equation .
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Step 6.1
Expand using the FOIL Method.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Apply the distributive property.
Step 6.1.3
Apply the distributive property.
Step 6.2
Simplify each term.
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Step 6.2.1
Multiply by .
Step 6.2.2
Multiply by .
Step 6.3
Expand by multiplying each term in the first expression by each term in the second expression.
Step 6.4
Simplify terms.
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Step 6.4.1
Simplify each term.
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Step 6.4.1.1
Multiply by by adding the exponents.
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Step 6.4.1.1.1
Multiply by .
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Step 6.4.1.1.1.1
Raise to the power of .
Step 6.4.1.1.1.2
Use the power rule to combine exponents.
Step 6.4.1.1.2
Add and .
Step 6.4.1.2
Move to the left of .
Step 6.4.1.3
Multiply by by adding the exponents.
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Step 6.4.1.3.1
Move .
Step 6.4.1.3.2
Multiply by .
Step 6.4.1.4
Multiply .
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Step 6.4.1.4.1
Multiply by .
Step 6.4.1.4.2
Raise to the power of .
Step 6.4.1.4.3
Raise to the power of .
Step 6.4.1.4.4
Use the power rule to combine exponents.
Step 6.4.1.4.5
Add and .
Step 6.4.1.5
Rewrite as .
Step 6.4.1.6
Multiply by .
Step 6.4.1.7
Move to the left of .
Step 6.4.1.8
Multiply by by adding the exponents.
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Step 6.4.1.8.1
Move .
Step 6.4.1.8.2
Multiply by .
Step 6.4.1.9
Multiply by .
Step 6.4.1.10
Multiply .
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Step 6.4.1.10.1
Multiply by .
Step 6.4.1.10.2
Raise to the power of .
Step 6.4.1.10.3
Raise to the power of .
Step 6.4.1.10.4
Use the power rule to combine exponents.
Step 6.4.1.10.5
Add and .
Step 6.4.1.11
Rewrite as .
Step 6.4.1.12
Multiply by .
Step 6.4.2
Simplify by adding terms.
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Step 6.4.2.1
Combine the opposite terms in .
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Step 6.4.2.1.1
Reorder the factors in the terms and .
Step 6.4.2.1.2
Subtract from .
Step 6.4.2.1.3
Add and .
Step 6.4.2.1.4
Reorder the factors in the terms and .
Step 6.4.2.1.5
Add and .
Step 6.4.2.1.6
Add and .
Step 6.4.2.2
Move .
Step 7