Question

Find the period,range, and amplitude of the cosine function. y= -5 cos 6 x

Answer 1

in general circular function such as
\[y=A\cos(Bx+C)+D\]
has amplitude A
period \[\frac{2\pi}{|B|}\]
phase shift c units to left
D upward shift

Answer 2

for the range we know that \[-1\le \cos x\le 1\]

Answer 3

The amplitude is -5 correct?

Answer 4

Wait or is it just 5?

Answer 5

so we can say that \[-1\le \cos 6x \le 1 \Longrightarrow -5\le -5 \cos 6x \le 5\]
\[-5 \le y \le 5\]

Answer 6

oh actually 5 sorry amplitude is absolute value

Answer 7

Then 1/6pi is the period right?

Answer 8

I meant 1/3.

Answer 9

2pi/6=pi/3

Answer 10

yea 1/3 pi is good

Answer 11

Thanks so much for your help!

Answer 12

np :)