How to plot the graph of f(x)=2 sin 4x?

1 Answer
Alan P.
Jul 22, 2015

Draw a standard sin curve but "squeeze" the vertical so the period is reduced from 2pi to pi/2 and stretch the horizontal so the amplitude is increased from [-1,1] to [-2, 2]

Explanation:

sin(theta) has a period of 2pi
replacing theta by 4x means that 4x must have the same period
and therefore each x of the 4x can only take up (2pi)/4 = pi/2 period length.

sin(theta) has an amplitude of [-1,+1]
rarr for any angle 4x, sin(4x) must be a value s epsilon [-1,+1]
and
rarr 2sin(4x) must be 2s giving it a range of [-2,+2]

Related questions
See all questions in Translating Sine and Cosine Functions
Impact of this question
2398 views around the world
You can reuse this answer
Creative Commons License