Question

How do you graph negative cosine?

Answer 1

Hint:
To draw the graph of the negative of cosine first draw the cosine graph then translate the graph . remember that negative cosine and cosine of negative angle are different. Because cosine of negative angle is positive means $\cos \left(-\theta \right)=\cos \left(\theta \right)$ but negative cosine is negative value of the cosine function that is $-\cos \left({\displaystyle \frac{\pi }{3}}\right)=-0.5$.

Complete step by step solution:
The objective of the problem is to draw the graph of negative cosine.
For that consider the interval $\left[-2\pi ,2\pi \right]$ and draw the graph of negative cosine in the interval $\left[-2\pi ,2\pi \right]$ and observe the pattern.

$\theta$	$-2\pi$	$-{\displaystyle \frac{3\pi }{2}}$	$-\pi$	$-{\displaystyle \frac{\pi }{2}}$	$0$	${\displaystyle \frac{\pi }{2}}$	$\pi$	${\displaystyle \frac{3\pi }{2}}$	$2\pi$
$\cos \theta$	1	0	-1	0	1	0	-1	0	1
$-\cos \theta$	-1	0	1	0	-1	0	1	0	-1

Draw the graph of negative cosine using graphing software

From the graph observe that the range of negative cosine is $\left[-1,1\right]$ and at every multiple of ${\displaystyle \frac{\pi }{2}}$ intersect the x-axis at zero and at every multiple of pi reaches one. At zero it reaches -1. This happens in every interval. Using this pattern we can extend the graph of negative sine for every segment .
The graph of negative cosine will be like this using graphing software.

Note:
The graph of negative cosine is the transpose of the graph of cosine. These waves are called sinusoidal waves. The value of cosine lies between minus one to plus one. The period of the cosine function is two pi. And for the sine function the period is also the same as the cosine function. And the values of sine function lies between minus one and plus one. Tan function period is pi.