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=tan−1(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=tan−1(yx)
Step 3
Step 3.1
Raise -2−2 to the power of 22.
r=√4+(9)2r=√4+(9)2
θ=tan-1(yx)θ=tan−1(yx)
Step 3.2
Raise 99 to the power of 22.
r=√4+81r=√4+81
θ=tan-1(yx)θ=tan−1(yx)
Step 3.3
Add 44 and 8181.
r=√85r=√85
θ=tan-1(yx)θ=tan−1(yx)
r=√85r=√85
θ=tan-1(yx)θ=tan−1(yx)
Step 4
Replace xx and yy with the actual values.
r=√85r=√85
θ=tan-1(9-2)θ=tan−1(9−2)
Step 5
The inverse tangent of -92−92 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°)