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Consider the graph of the cosine function shown below.

a. Find the period and amplitude of the cosine function.
b. At what values of θ for 0 ≤ θ ≤ 2π do the maximum value(s), minimum values(s), and zeros occur?

Consider the graph of the cosine function shown below a Find the period and amplitude of the cosine function b At what values of θ for 0 θ 2π do the maximum val class=

Respuesta :

Answer:

a. Amplitude: 4

Period: 1

b. The maximum values occur at [tex]\theta=0,1,2[/tex]

The minimum values occur at [tex]\theta=\frac{1}{2},\frac{3}{2}[/tex]

The zeros occur at [tex]\theta=\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4}[/tex]

Step-by-step explanation:

We can see from the graph that;

[tex]-4\le f(x) \le 4[/tex].

This implies that;

[tex]|A|=4[/tex].

The amplitude is 4.

The function also completed one full cycle on the interval [0,1]

The period is

[tex]T=|1-0|=1[/tex]

The maximum values occur at [tex]\theta=0,1,2[/tex]

The minimum values occur at [tex]\theta=\frac{1}{2},\frac{3}{2}[/tex]

The zeros occur at [tex]\theta=\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4}[/tex]

This is where the graph intersected the x-axis.