If (a,b)(a,b) is a are the coordinates of a point in Cartesian Plane, uu is its magnitude and alphaα is its angle then (a,b)(a,b) in Polar Form is written as (u,alpha)(u,α).
Magnitude of a cartesian coordinates (a,b)(a,b) is given bysqrt(a^2+b^2)√a2+b2 and its angle is given by tan^-1(b/a)tan−1(ba)
Let rr be the magnitude of (-2,5)(−2,5) and thetaθ be its angle.
Magnitude of (-2,5)=sqrt((-2)^2+5^2)=sqrt(4+25)=sqrt29=r(−2,5)=√(−2)2+52=√4+25=√29=r
Angle of (-2,5)=Tan^-1(5/(-2))=Tan^-1(-5/2)=-68.198(−2,5)=tan−1(5−2)=tan−1(−52)=−68.198 degree
implies⇒ Angle of (-2,5)=-68.198(−2,5)=−68.198 degree
But since the point is in second quadrant so we have to add 180180 degree which will give us the angle.
implies⇒ Angle of (-2,5)=-68.198+180=111.802(−2,5)=−68.198+180=111.802
implies⇒ Angle of (-2,5)=111.802=theta(−2,5)=111.802=θ
implies (-2,5)=(r,theta)=(sqrt29,111.802)⇒(−2,5)=(r,θ)=(√29,111.802)
implies (-2,5)=(sqrt29,111.802)⇒(−2,5)=(√29,111.802)
Note that the angle is given in degree measure.
