Question

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Answer 1

Explanation:

(5 rad 2, 135 degrees),(-5 rad 2, 315 degrees)

Answer 2

`\bf \begin{array}{llll} 5&,&-5\\ x&&y \end{array}\qquad \begin{cases} r=√(x^2+y^2)\\\\ \theta=tan^(-1)\left( (y)/(x) \right) \end{cases}\\\\ -----------------------------\\\\ r=√((5)^2+(-5)^2)\implies r√(50)\implies \boxed{r=5√(2)} \\\\\\ \theta=tan^(-1)\left( (-5)/(5) \right)\implies 0=tan^(-1)(-1)`

now.... the tangent is -1 when the "y" and "x" are of different signs
now, that happens in the 2nd and 4th quadrant, however, let's take a look at our terminal point, 5 , -5

the "x" is positive, the "y" is negative, that means, is the one on the 4th quadrant
`\bf \theta=(7\pi )/(4)`

thus
`\bf \left( 5√(2)\ ,\ (7\pi )/(4) \right)`