| $$ r=3*\sqrt2$$ | | | $$\theta = \frac{-\pi}{4}$$ | or | $$\frac{7\pi}{4}$$ |
Find r:
$$r = \sqrt{x^2+y^2}
= \sqrt{3^2+(-3)^2}
= \sqrt{9+9}
= \sqrt{18}$$
Find θ:
$$\theta = arctan(\frac{y}{x})
= arctan(\frac{-3}{3})
= arctan(-1)$$
$$tan(\frac{\pi}{4}) = 1$$
$$tan(-\frac{\pi}{4}) = -1 = tan(\frac{7\pi}{4})$$
Find x:
$$x = r*cos(\theta) = \sqrt{29}*cos(-0.38)$$
$$= \sqrt{29}*cos(0.38) = 5$$
Find y:
$$x = r*sin(\theta) = \sqrt{29}*sin(-0.38) $$
$$= \sqrt{29}*-sin(0.38) = -2$$