Question

Plot the x intercepts,maxima and minima of y=cos(x) from 0 to 2pi

Answer 1

Answer:

Figure of the function is included below as attachment.

Step-by-step explanation:

Let $y = \cos x$As first step we have to find x intercepts, maxima and minima from 0 to 2π, which are needed to plot given function. Cosine is a trigonometric function bounded between -1 and 1 with a periodicity of 2π.

x-Intercepts

x-intercepts are those points of the function such that $y = 0$. That is:

$\cos x = 0$

In this case, there is a periodicity of π for $y = 0$. The x-intercepts are in the following set:

$S = \{\forall\,x\in\mathbb{R}|x=0.5\pi\pm\pi\cdot i,i\in\mathbb{N}_{O} \}$

Maxima

Maxima are those points of the function such that $y = 1$. That is:

$\cos x = 1$

In this case, there is a periodicity of 2π for $y = 1$. Maxima are in the following set:

$S = \{\forall\,x\in\mathbb{R}|x=0\pm2\pi\cdot i,i\in\mathbb{N}_{O} \}$

Minima

Minima are those points of the function such that $y = -1$. That is:

$\cos x = -1$

In this case, there is a periodicity of 2π for $y = -1$. Minima are in the following set:

$S = \{\forall\,x\in\mathbb{R}|x=\pi\pm2\pi\cdot i,i\in\mathbb{N}_{O} \}$

Lastly, we proceed to plot the function as well as its x-intercepts, maxima and minima with the help of a plotting tool.