## Trigonometry (11th Edition) Clone

(a) $x = 3~cos~t$ $y = 3~sin~t$ We can see the graph below. (b) $x^2+y^2 = 9$
(a) $x = 3~cos~t$ $y = 3~sin~t$ When $t = 0$: $x = 3~cos~0 = 3$ $y = 3~sin~0 = 0$ When $t = \frac{\pi}{6}$: $x = 3~cos~\frac{\pi}{6} = \frac{3\sqrt{3}}{2}$ $y = 3~sin~\frac{\pi}{6} = \frac{3}{2}$ When $t = \frac{\pi}{4}$: $x = 3~cos~\frac{\pi}{4} = \frac{3\sqrt{2}}{2}$ $y = 3~sin~\frac{\pi}{4} = \frac{3\sqrt{2}}{2}$ When $t = \frac{\pi}{3}$: $x = 3~cos~\frac{\pi}{3} = \frac{3}{2}$ $y = 3~sin~\frac{\pi}{3} = \frac{3\sqrt{3}}{2}$ When $t = \frac{\pi}{2}$: $x = 3~cos~\frac{\pi}{2} = 0$ $y = 3~sin~\frac{\pi}{2} = 3$ When $t = \frac{2\pi}{3}$: $x = 3~cos~\frac{2\pi}{3} = -\frac{3}{2}$ $y = 3~sin~\frac{2\pi}{3} = \frac{3\sqrt{3}}{2}$ When $t = \pi$: $x = 3~cos~\pi = -3$ $y = 3~sin~\pi = 0$ When $t = \frac{4\pi}{3}$: $x = 3~cos~\frac{4\pi}{3} = -\frac{3}{2}$ $y = 3~sin~\frac{4\pi}{3} = -\frac{3\sqrt{3}}{2}$ When $t = \frac{3\pi}{2}$: $x = 3~cos~\frac{3\pi}{2} = 0$ $y = 3~sin~\frac{3\pi}{2} = -3$ We can see the graph below. (b) $x = 3~cos~t$ $y = 3~sin~t$ $x^2+y^2 = (3~cos~t)^2+(3~sin~t)^2$ $x^2+y^2 = 9~cos^2~t+9~sin^2~t$ $x^2+y^2 = 9~(cos^2~t+~sin^2~t)$ $x^2+y^2 = 9~(1)$ $x^2+y^2 = 9$