Precalculus Examples

Convert to Polar Coordinates (2 square root of 3,-2)
Step 1
Convert from rectangular coordinates to polar coordinates using the conversion formulas.
Step 2
Replace and with the actual values.
Step 3
Find the magnitude of the polar coordinate.
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Step 3.1
Simplify the expression.
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Step 3.1.1
Apply the product rule to .
Step 3.1.2
Raise to the power of .
Step 3.2
Rewrite as .
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Step 3.2.1
Use to rewrite as .
Step 3.2.2
Apply the power rule and multiply exponents, .
Step 3.2.3
Combine and .
Step 3.2.4
Cancel the common factor of .
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Step 3.2.4.1
Cancel the common factor.
Step 3.2.4.2
Rewrite the expression.
Step 3.2.5
Evaluate the exponent.
Step 3.3
Simplify the expression.
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Step 3.3.1
Multiply by .
Step 3.3.2
Raise to the power of .
Step 3.3.3
Add and .
Step 3.3.4
Rewrite as .
Step 3.3.5
Pull terms out from under the radical, assuming positive real numbers.
Step 4
Replace and with the actual values.
Step 5
The inverse tangent of is .
Step 6
This is the result of the conversion to polar coordinates in form.