Trigonometry Examples

Find the Equation Given the Roots -2 , 0 , 3+2i
, ,
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
The root at was found by solving for when and .
The factor is
Step 6
Combine all the factors into a single equation.
Step 7
Multiply all the factors to simplify the equation .
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Step 7.1
Simplify by multiplying through.
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Step 7.1.1
Apply the distributive property.
Step 7.1.2
Multiply by .
Step 7.2
Expand by multiplying each term in the first expression by each term in the second expression.
Step 7.3
Simplify terms.
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Step 7.3.1
Simplify each term.
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Step 7.3.1.1
Multiply by by adding the exponents.
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Step 7.3.1.1.1
Multiply by .
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Step 7.3.1.1.1.1
Raise to the power of .
Step 7.3.1.1.1.2
Use the power rule to combine exponents.
Step 7.3.1.1.2
Add and .
Step 7.3.1.2
Move to the left of .
Step 7.3.1.3
Multiply by by adding the exponents.
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Step 7.3.1.3.1
Move .
Step 7.3.1.3.2
Multiply by .
Step 7.3.1.4
Multiply by .
Step 7.3.1.5
Multiply by .
Step 7.3.2
Add and .
Step 7.4
Expand by multiplying each term in the first expression by each term in the second expression.
Step 7.5
Simplify terms.
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Step 7.5.1
Simplify each term.
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Step 7.5.1.1
Multiply by by adding the exponents.
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Step 7.5.1.1.1
Multiply by .
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Step 7.5.1.1.1.1
Raise to the power of .
Step 7.5.1.1.1.2
Use the power rule to combine exponents.
Step 7.5.1.1.2
Add and .
Step 7.5.1.2
Move to the left of .
Step 7.5.1.3
Move to the left of .
Step 7.5.1.4
Multiply by by adding the exponents.
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Step 7.5.1.4.1
Move .
Step 7.5.1.4.2
Multiply by .
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Step 7.5.1.4.2.1
Raise to the power of .
Step 7.5.1.4.2.2
Use the power rule to combine exponents.
Step 7.5.1.4.3
Add and .
Step 7.5.1.5
Multiply by .
Step 7.5.1.6
Multiply by .
Step 7.5.1.7
Multiply by by adding the exponents.
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Step 7.5.1.7.1
Move .
Step 7.5.1.7.2
Multiply by .
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Step 7.5.1.7.2.1
Raise to the power of .
Step 7.5.1.7.2.2
Use the power rule to combine exponents.
Step 7.5.1.7.3
Add and .
Step 7.5.1.8
Multiply by .
Step 7.5.1.9
Move to the left of .
Step 7.5.1.10
Multiply .
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Step 7.5.1.10.1
Multiply by .
Step 7.5.1.10.2
Raise to the power of .
Step 7.5.1.10.3
Raise to the power of .
Step 7.5.1.10.4
Use the power rule to combine exponents.
Step 7.5.1.10.5
Add and .
Step 7.5.1.11
Rewrite as .
Step 7.5.1.12
Multiply by .
Step 7.5.1.13
Move to the left of .
Step 7.5.1.14
Multiply by by adding the exponents.
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Step 7.5.1.14.1
Move .
Step 7.5.1.14.2
Multiply by .
Step 7.5.1.15
Multiply by .
Step 7.5.1.16
Multiply by .
Step 7.5.1.17
Multiply by by adding the exponents.
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Step 7.5.1.17.1
Move .
Step 7.5.1.17.2
Multiply by .
Step 7.5.1.18
Multiply by .
Step 7.5.1.19
Multiply .
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Step 7.5.1.19.1
Multiply by .
Step 7.5.1.19.2
Raise to the power of .
Step 7.5.1.19.3
Raise to the power of .
Step 7.5.1.19.4
Use the power rule to combine exponents.
Step 7.5.1.19.5
Add and .
Step 7.5.1.20
Rewrite as .
Step 7.5.1.21
Multiply by .
Step 7.5.2
Simplify by adding terms.
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Step 7.5.2.1
Combine the opposite terms in .
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Step 7.5.2.1.1
Reorder the factors in the terms and .
Step 7.5.2.1.2
Subtract from .
Step 7.5.2.1.3
Add and .
Step 7.5.2.1.4
Add and .
Step 7.5.2.1.5
Add and .
Step 7.5.2.2
Subtract from .
Step 7.5.2.3
Add and .
Step 7.5.2.4
Subtract from .
Step 7.5.2.5
Add and .
Step 7.5.2.6
Combine the opposite terms in .
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Step 7.5.2.6.1
Subtract from .
Step 7.5.2.6.2
Add and .
Step 7.5.2.7
Add and .
Step 8