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

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

Printable View

- May 5th 2010, 01:29 AMmastermin346GRAPH OF COSine FUNCTION
sketch the graph of cosine for $\displaystyle 0<\theta<2\pi$

$\displaystyle y=2-\mid cos\frac{\theta}{2}\mid$ - May 5th 2010, 04:04 AMTheCoffeeMachine
Note that $\displaystyle 2-\bigg|\cos\left(\dfrac{\theta}{2}\right)\bigg| = 2-\sqrt{\cos^2\left(\dfrac{\theta}{2}\right)}$ (Wink)

- May 5th 2010, 04:41 AMmathaddict
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 . - May 5th 2010, 04:58 AMArchie Meade
$\displaystyle cos(0)=1$

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

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

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

or it has half the frequency.

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