6. The point $Q(-3,6)$ is on the terminal arm of an angle, $\theta$. a) Draw this angle in standard position. b) Determine the exact distance from the origin to point $Q$. c) Determine the exact values for $\sin \theta$, $\cos \theta$, and $\tan \theta$. d) Determine the value of $\theta$.

Step 1 ：\(Q(-3,6)\) is on the terminal arm of angle \(\theta\) in standard position.

Step 2 ：Calculate the distance from the origin to point \(Q\) using the distance formula: \(d = \sqrt{(-3)^2 + 6^2}\)

Step 3 ：\(d = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}\)

Step 4 ：\(\sin \theta = \frac{6}{3\sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2\sqrt{5}}{5}\)

Step 5 ：\(\cos \theta = \frac{-3}{3\sqrt{5}} = \frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}\)

Step 6 ：\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{2\sqrt{5}}{5}}{\frac{-\sqrt{5}}{5}} = -2\)

Step 7 ：\(\theta = \arctan(-2)\) in Quadrant II

Step 8 ：\(\theta = \boxed{180^\circ - \arctan(2)}\)