What is the polar form of (-1,12)(−1,12)?

1 Answer
A. S. Adikesavan
Mar 30, 2016

(sqrt145, 94.76^o)(√145,94.76o)

Explanation:

x=-1, y=12;r = sqrt(x^2+y^2)=sqrt145x=−1,y=12;r=√x2+y2=√145.

thetaθ satisfying both cos theta=x/r=-1/sqrt145cosθ=xr=−1√145 and sin theta =y/r=12/sqrt145sinθ=yr=12√145 is

94,76^o#,
in the second quadrant in which cosine is negative and sine is positive.

sin (180^o-theta)=sin thetasin(180o−θ)=sinθ. Calculator display for sin^(-1)(12/sqrt145)sin−1(12√145) is 85.24^o85.24o, nearly.
Choose theta = 180^o-85.24^o=94.76^o=cos^(-1)(-1/sqrt145)θ=180o−85.24o=94.76o=cos−1(−1√145).

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