Question

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

Answer 1

$$
\text{from (3,-3) we can see that x=3, y=-3; THEN}\\
\text{you want to get the polar coords of (radius, angle) pair}\\
\text{using pythagorean identity } r^2=x^2+y^2\\
r=\sqrt{(3)^2+(-3)^2} \implies r=\sqrt{18} \implies \boldsymbol{r=2\sqrt{3}}\\
\text{now to find the angle } tan(\theta)=\cfrac{y}{x} \\
tan(\theta)=\cfrac{-3}{3}=-1 \implies tan(tan\theta)^{-1}=tan(-1)^{-1}
$$

Answer 2

can you get that angle WHOSE tangent is -1?