How trigonometric ratios fit into equations when dealing with sinusoidal waves

[ChrisHansen2Legit2Quit]

Does anyone know any sources that can explain how sin fits into a function?

I keep seeing f(x)=sin ...w(t) or something.

I understand oscillations, freq, amplitude, etc... but Im not sure how ratios of angles to lengths in triangles have found their way into the equations that I see pop up time to time.

 

[LvW]

I am not sure if this answers your question:
Sinusoidal signals can be expressed by exponenetial functions like Vin=Vo*exp[j(wt+phi,1)].
If such a signal is applied to a frequency-dependent network (filter, amplifier) the output will change in magnitude and phase like Vout=A*Vo*exp[j(wt+phi,2)].
Thus, the gain is Vout/Vin=A*exp[j(phi,1-phi,2)].
Thus, you have the DIFFERENCE of two angles (but not a ratio).

 

[albbg]

Does anyone know any sources that can explain how sin fits into a function?

I keep seeing f(x)=sin ...w(t) or something.

I understand oscillations, freq, amplitude, etc... but Im not sure how ratios of angles to lengths in triangles have found their way into the equations that I see pop up time to time.

Could you elaborate a litte bit more your question ?

 

[ChrisHansen2Legit2Quit]

The sine and cosine are the protections of a line of length equal to 1 onto either the Y axis or X axis. So if the line is on the X axis it has an angle of zero it measures 1 along the X, the cosine tells you how long the line and so cos(0) = 1. If the line is moved 15 degrees then cos(15) = .97 meaning if you drew a straight line to the x-axis the length on the x-axis would be .97 long. The sine is just 1-cos() so it is what the line measures on the Y-axis. This is why sin(45) = cos(45) because the line at 45 degrees projects an equal amont on both the X and Y axis.

This was taken from another forum, and it's the best explanation I have yet to come across. Most youtube videos just go straight into application -noy so much explaining soacahtoa

If anyone has a link, please lmk. Thanks!