How to transform trigonometric functions

Answer 1

Hi,

I am assuming that you are asking about transformations such as translations, stretches, and compressions.

For the function sin(x), we can think of several transformations:

y = sin(x) + b translates the sin function up by b units

y = sin(x-λ) shifts the sine function to the right by λ

special case: sin(x-(π/2)) = cos(x)

y = sin(x+λ) shifts the sine function to the left by λ

y = A sin(x) stretches the amplitude of the function by a factor of A

So far, this seems exactly like how we transformed non-trig functions in algebra. But there is one cool thing you can do with trig functions that is important for modeling things like waves and oscillators (springs, pendulums, etc) in physics:

y = sin(nx) changes the wavelength of the sine function by a factor of 1/n

There are more transformations and significant physical meanings to consider when trig functions such as sine are functions of both space (x) and time (t) in physics, but I think this covers the basic idea of trig transformations for now.