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What is the polar form of #( 10,12 )#?

Answer 1

Emilia Aguilar

#(15.62,50.19^@)#

we know, polar form of a point is #(r,theta)#

#r=sqrt(x^2+y^2)#

#=sqrt(10^2+12^2)#

#=sqrt(244)#

#=15.62#

#theta=tan^(-1)(12/(10))#

#=tan^(-1)(1.2)#

#=50.19^@#

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Answer 2

Charles Arocha

The polar form of the point (10,12) is given by ( (r, \theta) ), where ( r ) represents the distance from the origin to the point and ( \theta ) represents the angle formed by the positive x-axis and the line connecting the point to the origin. To find ( r ) and ( \theta ), we can use the formulas:

[ r = \sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{y}{x}\right) ]

Substituting the given values ( x = 10 ) and ( y = 12 ):

[ r = \sqrt{10^2 + 12^2} = \sqrt{100 + 144} = \sqrt{244} ]

[ \theta = \arctan\left(\frac{12}{10}\right) = \arctan\left(\frac{6}{5}\right) ]

Thus, the polar form of the point (10,12) is ( (\sqrt{244}, \arctan\left(\frac{6}{5}\right)) ).

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Answer from HIX Tutor

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