1. GRAPH OF COSine FUNCTION

sketch the graph of cosine for $0<\theta<2\pi$

$y=2-\mid cos\frac{\theta}{2}\mid$

2. Note that $2-\bigg|\cos\left(\dfrac{\theta}{2}\right)\bigg| = 2-\sqrt{\cos^2\left(\dfrac{\theta}{2}\right)}$

3. Originally Posted by mastermin346
sketch the graph of cosine for $0<\theta<2\pi$

$y=2-\mid cos\frac{\theta}{2}\mid$
hi

first off , do you know how to sketch the graph of cos 1/2 Θ ?

Note that its period is 2π/(1/2)=4π

The usual graph we draw (cos Θ) has a period of 2π but this time , 4π .

|cos 1/2 Θ| - reflect the negative part of the graph to the postive side

- |cos 1/2 Θ| - reflect the whole graph about the x-axis

2 - |cos 1/2 Θ| - shift the graph up by 2 units .

4. Originally Posted by mastermin346
sketch the graph of cosine for $0<\theta<2\pi$

$y=2-\mid cos\frac{\theta}{2}\mid$
$cos(0)=1$

$cos\left(\frac{{\pi}}{2}\right)=0$

$cos\left(\frac{\theta}{2}\right)=0\ \Rightarrow\ \frac{\theta}{2}=\frac{{\pi}}{2}\ \Rightarrow\ \theta={\pi}$

$cos\left(\frac{\theta}{2}\right)$ has twice the period that $cos\theta$ has

or it has half the frequency.

Knowing that, the graph can be drawn using $cos\theta$ to guide.