Question

Sketch one cycle of the cosine function. y = 2 cos 2 theta

Answer 1

One cycle is of period π.

Explanation:

Given : Cosine function
`y=2\cos 2\theta`

To find : Sketch one cycle of the cosine function ?

Solution :

The general form of cosine function is
`y=a \cos (bx-c)+d`

On comparing with
`y=2\cos 2\theta`

a=2 , b=2 , c=0, d=0

Where, Amplitude is
`|a|=|2|`

Amplitude = 2

`\text{Period}=(2\pi)/(|B|)`

`\text{Period}=(2\pi)/(|2|)`

`\text{Period}=\pi`

Phase shift and vertical shift is zero.

Therefore, One cycle is of period π.

Refer the attached figure below.

Answer 2

So the question ask to sketch the one cycle of the cosine function where as the y = 2cos theta. So base on the function, its just and ordinary graph but the data is not the same. The line begins at the positive 2 in the Y axis then goes down with constant magnitude after it reach its limit it goes up again with constant magnitude and its limit in negative y axis is -2.