Precalculus Examples

(-2,9)(2,9)
Step 1
Convert from rectangular coordinates (x,y)(x,y) to polar coordinates (r,θ)(r,θ) using the conversion formulas.
r=x2+y2r=x2+y2
θ=tan-1(yx)θ=tan1(yx)
Step 2
Replace xx and yy with the actual values.
r=(-2)2+(9)2r=(2)2+(9)2
θ=tan-1(yx)θ=tan1(yx)
Step 3
Find the magnitude of the polar coordinate.
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Step 3.1
Raise -22 to the power of 22.
r=4+(9)2r=4+(9)2
θ=tan-1(yx)θ=tan1(yx)
Step 3.2
Raise 99 to the power of 22.
r=4+81r=4+81
θ=tan-1(yx)θ=tan1(yx)
Step 3.3
Add 44 and 8181.
r=85r=85
θ=tan-1(yx)θ=tan1(yx)
r=85r=85
θ=tan-1(yx)θ=tan1(yx)
Step 4
Replace xx and yy with the actual values.
r=85r=85
θ=tan-1(9-2)θ=tan1(92)
Step 5
The inverse tangent of -9292 is θ=102.5288077°θ=102.5288077°.
r=85r=85
θ=102.5288077°θ=102.5288077°
Step 6
This is the result of the conversion to polar coordinates in (r,θ)(r,θ) form.
(85,102.5288077°)(85,102.5288077°)
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