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?

a.

Period = π

Amplitude = 4

b.

Maximum at: x = 0, π and 2π

Minimum at: x = π/2 and 3π/2

Zeros at: x = π/4, 3π/4, 5π/4 and 7π/4

Step-by-step explanation:

Part a:

Amplitude represents the half of the distance between the maximum point and the minimum point of the function. So the easy way to find the amplitude is: Find the difference between maximum and minimum value of the function and divide the difference by 2.

So, amplitude will be:

Therefore, the amplitude of the function is 4.

Period is the time in which the function completes its one cycle. From the graph we can see that cosine started at 0 and completed its cycle at π. After π the same value starts to repeat. So the period of the given cosine function is π.

Part b:

From the graph we can see that the maximum values occur at the following points: x = 0, π and 2π

The scale on x-axis between 0 and π is divided into 4 squares, so each square represents π/4

Therefore, the minimum value occurs at x = π/2 and 3π/2

Zeros occur where the graph crosses the x-axis. So the zeros occur at the following points: π/4, 3π/4, 5π/4 and 7π/4

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