What is the polar form of ( -34,99 )?

Aug 4, 2017

$\left(104.676 , 1.902\right)$

Explanation:

We're asked to find the polar coordinate of a given Cartesian coordinate.

To do this, we can use the the equations

ul(r^2 = x^2 + y^2

ul(theta = arctan(y/x)

for the polar coordinate $\left(r , \theta\right)$

Here,

$x = - 34$

$y = 99$

So we have

${r}^{2} = {\left(- 34\right)}^{2} + {99}^{2}$

r = sqrt((-34)^2 + 99^2) = color(red)(ulbar(|stackrel(" ")(" "104.676" ")|)

The argument $\theta$ will be

$\theta = \arctan \left(\frac{99}{- 34}\right) = \underline{- 1.240}$ OR ul(1.902 (both in radians)

Arctangent calculations will give two answers, each a half-circle ($\pi$/${180}^{\text{o}}$) apart, so be sure to know which one it is.

Here, the $x$-coordinate is negative and the $y$-coordinate is positive, so the angle must be in quadrant II (i.i. the angle must be betwen $\frac{\pi}{2}$ and $\pi$).

Thus,

color(red)(ulbar(|stackrel(" ")(" "theta = 1.902" ")|)

So the polar coordinate is

color(blue)((104.676, 1.902)