What is the period of y = 4 sin 3x ?

Amplitude of

4

sin

(

3

x

)

is

4

Period of

4

sin

(

3

x

)

is

6

π

Explanation:

y

=

sin

(

θ

)

has an amplitude of

1

y

varies between

+

1

and

−

1

If

y

=

4

sin

(

θ

)

then

y

will vary between

+

4

and

−

4

→

y

=

4

sin

(

θ

)

has an amplitude of

4

(for any

θ

)

y

=

k

⋅

sin

(

θ

)

has a period of

2

π

y

completes one cycle while

θ

increases by

2

π

if

3

x

=

θ

y

completes one cycle while

3

x

increases by

2

π

or (expressed in another way)

y

completes

1

3

of a cycle while

x

increase by

2

π

⇒

y

completes 1 cycle while

x

increases by

3

×

2

π

=

6

π

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step-by-step explanation:

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step-by-step explanation: