Verified Answer :

meerkat18

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.

Answer:

One cycle is of period π.

Step-by-step 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

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

\(\text{Period}=\frac{2\pi}{|2|}\)

\(\text{Period}=\pi\)

Phase shift and vertical shift is zero.

Therefore, One cycle is of period π.

Refer the attached figure below.

View image tardymanchester

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