Answer:
At [tex]\frac{\pi}{2}and\frac{3\pi}{2}[/tex] the graph of f(x) = cos x intersect the x-axis.
Step-by-step explanation:
Given the function f(x)=cosx
We have to choose the value of x for which the graph intersect the x-axis.
The graph intersect the x-axis when at any point of x value of y i.e f(x) is 0.
Hence, [tex]f(0)=cos0=1[/tex]
[tex]f(\frac{\pi}{2})=cos(\frac{\pi}{2})=0[/tex]
[tex]f(\pi)=cos(\pi)=-1[/tex]
[tex]f(\frac{3\pi}{2})=0[/tex]
[tex]cos(2\pi)=1[/tex]
At two values of x i.e at π/2 and 3π/2 the value of y is 0.
Hence, at [tex]\frac{\pi}{2}and\frac{3\pi}{2}\text{the graph of f(x) = cos x intersect the x-axis}[/tex]
The two values of x at which the function intercepts the x-axis are:
x = π/2 and x = 3π/2
A function f(x) intercepts the x-axis for a value x₀ if:
f(x₀) = 0
So here we must find the value of x such that:
f(x) = cos(x) = 0.
This is really well known, we know that for any integer number n:
cos( (2n + 1)*π/2) = 0
So we must find the values:
x = (2n + 1)*π/2
Particularly, if we take n = 0 we get:
x = (2*0 + 1)*π/2 = π/2
And if we take n = 1 we et:
x = (2*1 + 1)*π/2 = 3π/2
Then, from the given values, the two x-values at which the function intercepts the x-axis are:
x = π/2 and x = 3π/2
If you want to learn more about x-intercepts, you can read:
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