Question

y = 3 sin(2x)
In this, would the 2 be the period?

Answer 1

2x = 2(pi) (normal sin period)
So that means the period of 2x would be solving for x. So divide both sides by 2 and you get simply pi.

Answer 2

...What?

Answer 3

Sorry. Im sure sami has a better answer for ya.

Answer 4

period of sin(x) is 2pi
generally if
\[\Large \sin(ax)\]
then period will be
\[\Large \frac{2\pi}{a}\]
here in
3sin(2x) a=2
can you find it now ?

Answer 5

...No. I'm even more confused.

Answer 6

hehhe

Answer 7

let me give you few examples
just remember the formula
if
\[\Large \sin(ax)\]
period is given by \[\Large \frac{2\pi}{a}\]

Examples
1) period of sin(5x) is \[\Large \frac{2\pi}{5}\] because a=5 here
2) period of sin(3x) \[\Large \frac{2\pi}{3}\] because a=3 here
3) period of sin(7x) is \[\Large \frac{2\pi}{7}\] because a=7 here

can you now find the period of 3sin(2x) ?

Answer 8

(2pi)/2???

Answer 9

yes

Answer 10

or you can say pi as 2 will be cancellled with 2

Answer 11

Ohhh.
What about amplitudes?

Answer 12

amplitute is affeted by the constant multiplied with it

for example
bsin(ax) here period is 2pi/a and amplitude is b
so

1) 2sin(5) amplitude is 2
2) 3sin(7x) amplitude is 3
3) 6 sin(2x) amplitude is 6

so just remember whats inside the parenthesis contributes to period and the constant bieng multiplied decide the amplitude


can you now find the amplitude of 3sin(2x) ?

Answer 13

3

Answer 14

yup

Answer 15

What if you wanna find a period of something that is like y = 1/3cos(x/2 )?