Question

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

Answer 1

Figure of the function is included below as attachment.

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.