How do you convert (-2, 5)(−2,5) to polar form?

1 Answer
turksvids
Dec 10, 2017

(sqrt(29), pi-tan^(-1)(5/2))(√29,π−tan−1(52)) or (-sqrt(29), tan^(-1)(-5/2))(−√29,tan−1(−52))

Explanation:

To convert rectangular (a,b)(a,b) to polar we use the two formulas:

r=sqrt(a^2+b^2)r=√a2+b2 and hat theta=tan^(1)(|b/a|)ˆθ=tan1(∣∣∣ba∣∣∣)

then we have to "fix" the quadrant for thetaθ.

r=sqrt((-2)^2+5^2)=sqrt(29)r=√(−2)2+52=√29

hat theta = tan^(-1)(5/2)ˆθ=tan−1(52)

the point (-2,5)(−2,5) is in QII, so theta = pi-hat thetaθ=π−ˆθ

therefore theta = pi-tan^(-1)(5/2)θ=π−tan−1(52).

An alternate, but equivalent representation is (-sqrt(29), tan^(-1)(-5/2))(−√29,tan−1(−52)), which uses a QIV angle but a negative rr to end up in QII.

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