Negative Cosine Graph

Basically if we draw the cosine graph mean the graph will like a normal graph. Negative cosine graph is nothing but the negative sign in front of the cos.  A negative cosine equation will be like the following

Y = - a cos (bx +c)

Hare – sign is in front of the cosine graph. If we draw the negative cosine it will produce the reflection about the x – axis. So the negative cosine graph will be opposite to the positive graph.

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Comparison between Positive and Negative Cosine Graphs:

Let us any cosine function y = ± Cos ((2πx + 3))

Solution:

We want to draw the graph for both positive and negative cosine function.

Here phase shift = -c / b = -3 / 2π = -`1.5 / pi`

Period = 2π / b = 2π / 2π = 1

So the positive cosine graph will be like the following



And the negative cosine graph will be like the following



To know the difference we have to combine these two graphs. So we get



From the above we know the positive cosine graph will reflect the negative cosine graph. Here the red line graph indicates positive cosine graph and the black line graph indicates the negative cosine graph.

Example for Negative Cosine Graph:

Example 1:

Draw the graph for the following function y = - 5 Cos x

Solution:

Here the amplitude is 5 and this is having a negative sign with it. So it is a negative cosine graph. Here the period is 2π and there is no  phase shift. So the graph will be



Example 2:

Draw the graph for the following function y = - 0.5 Cos (π x / 6)

Solution:

Here the amplitude is 0.5 and this is having a negative sign with it. So it is a negative cosine graph. Here the period is 2π / (π / 6) = 12 and there is no phase shift. So the graph will be