Question

Consider the graph of the cosine function shown below.

Answer 1

this is not \(\cos(x)\) this is \(4\cos(2x)\)

Answer 2

oh sorry, what was the question?

Answer 3

Oops my bad. Find the period and amplitude of the cosine function.

Answer 4

if the question was "what function is this" then i gave away the answer

Answer 5

ok amplitude you see with your eyeballs
cosine goes from 1 to minus 1, with amplitude 1
this one goes from 4 to minus 4, so amplitude is ___ ?

Answer 6

4

Answer 7

ok good, and that is why i knew it was \(y=4\cos(bx)\)
period you also see with your eyeballs
can you see it?

Answer 8

Then at what values of theta for \[0 \le \theta \le 2 \pi\] do the maximum value(s), minimum values(s), and zeros occur?

Answer 9

lets get the period first, your last question is trivial
max is 4, min is -4 and you can see what value of \(x\) gets it

do you see the period?

Answer 10

is the period 0?

Answer 11

?

Answer 12

wheres the period

Answer 13

period is a length, the length over the \(x\) axis for which the function repeats

Answer 14

oh so its 4

Answer 15

for sine and cosine the period is \(2\pi\) because \(\sin(x)=\sin(x+2\pi)\)

Answer 16

oh no lets go slow
the amplitude is 4

Answer 17

period is the length from \(a\) to \(b\)

Answer 18

its 2

Answer 19

your function pictured goes from 4 to -4 and back up to 4 all in an interval of length \(\pi\)

Answer 20

2 pi