Question

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

Answer 1

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)")`