Question

Consider the graph of the cosine function shown below.
y= 4cos(2x)
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?

Answer 1

What are the period and amplitude of \(y = \cos(x)\)

Answer 2

the period of this equation is pie and the amplitude is 4

Answer 3

i just dont know how to get the answers to part b

Answer 4

The maximum and minimum of a normal cosine function are 1 (where the amplitude is 1), and since you have an amplitude of 4, you know that the y values for the maxes and mins will be 4.
The period of a normal cosine function is 2pi, and you should know where those zeros occur (pi/2, 3pi/2). This function is half as long (period is only pi) so each of the zeros is half as far, meaning they're at pi/4 and 3pi/4.
Same applies to find maxes and mins, the maxes of normal cosine are at 0 and 2pi, min at pi. These are all half as far, so the maxes are at 0 and pi, and the min is at pi/2.
Your maxes are (0,4), (2pi, 4) and min at (pi/2, -4)

Answer 5

1) "pie" is for eating and "pi" is for mathematics an greek spellers.
2) Develop systematic thinking.

\(y = \cos(x)\)

Period: \(2\pi\)
Amplitude: 1
Zeros: \(x = \pi/2+k\pi\)
Min: \(x = \pi + 2k\pi\)
Max: \(x = 0 + 2k\pi\)

\(y = 4\cos(x)\)

Period: \(2\pi\)
Amplitude: 4
Zeros: \(x = \pi/2+k\pi\)
Min: \(x = \pi + 2k\pi\)
Max: \(x = 0 + 2k\pi\)

\(y = 4\cos(2x)\)

Period: \(\pi\)
Amplitude: 4
Zeros: \(x = \pi/4+k\pi/2\)
Min: \(x = \pi/2 + k\pi\)
Max: \(x = 0 + k\pi\)

Don't be afraid to write stuff out!