<ol class="abc-list" start="5"><li><div class="list-item-content"><span class="list-item-text">Sketch the curve whose parametric equations are $x=2\cos t\cos 2t$, $y=\sin t\cos 2t$, $0\le t<2\pi $.</span></div></li></ol>

Sketch the curve whose parametric equations are $x=2\cos t\cos 2t$, $y=\sin t\cos 2t$, $0\le t<2\pi $.

Parametric Equations

Graphing Techniques

International Baccalaureate Higher Level Mathematics

IB HL Math

HCI Tutorial 2A Graphs and Transformations Q4

The curve passes through:
- $(0, 1)$ at $t = \frac{\pi}{2}$
- $(0, -1)$ at $t = \frac{3\pi}{2}$
- $(-2, 0)$ at $t = \pi$
- $(2, 0)$ at $t = 0$
- Origin $(0, 0)$ at $t = \frac{\pi}{4}$

**Finding x-intercepts (when $y = 0$):**
$y = 0 \Rightarrow \sin t \cdot \cos 2t = 0$
$\sin t = 0 \quad \text{or} \quad \cos 2t = 0$

For $\sin t = 0$:
$t = 0, \pi, 2\pi, 3\pi, ...$

For $\cos 2t = 0$:
$2t = \frac{\pi}{2}, \frac{3\pi}{2}, ...$
$t = \frac{\pi}{4}, \frac{3\pi}{4}, ...$

HCI Tutorial 2A Graphs and Transformations Q4

HCI Tutorial 2A Graphs and Transformations Q4

Video Solution: