Question

Question #8a89a

Answer 1

Use the equations, `r = sqrt(x^2 + y^2)` and `theta = pi + tan^-1(y/x)`
`(-3sqrt(3), -3) to (6, (7pi)/6)`

Explanation:

Given the point:

Use the equation:

`r = sqrt(x^2 + y^2`

`r = sqrt((-3sqrt(3))^2 + (-3)^2)`

`r = sqrt(27 + 9)`

`r = 6`

There are many equations for the angle, `theta`; which one you use depends on x and y:

`"[1] "theta = tan^-1(y/x); x > 0 and y ge 0`
`"[2] "theta = pi/2; x = 0 and y > 0`
`"[3] " theta = pi + tan^-1(y/x); x < 0`
`"[4] "theta = (3pi)/2; x = 0 and y < 0`
`"[5] "theta = 2pi + tan^-1(y/x); x > 0 and y < 0`

Because `x = -3sqrt(3)`, then we do not care about the value of y and we use equation [3}:

`theta = pi + tan^-1((-3)/(-3sqrt(3))); x < 0`

`theta = (7pi)/6`