What is the polar form of #( -1,121 )#?

1 Answer
Jan 23, 2016

Rectangular form: #(-1,121) hArr # Polar form: #(sqrt(14642),"arccos"(-1/sqrt(14642)))#

Explanation:

Radius is given by the Pythagorean Theorem as
#color(white)("XXX")r=sqrt(x^2+y^2)#

For the given values #(x,y)=(-1,121)#
#color(white)("XXX")r=sqrt((-1)^1+121^2) = sqrt(14642)#

The given point is in Quadrant II, so it is convenient to use the cos/arccos" functions.
#color(white)("XXX")cos(theta)=x/r#

#color(white)("XXX")rarr theta = "arccos"(x/r)#

#color(white)("XXXXXX")="arccos" ((-1)/sqrt(14642))#

Note: If this had any practical applications we would probably convert the above values into (approximate) values (using a calculator) as
#color(white)("XXX")(r,theta)~=(121,1.58 " (radians)")#