trigonometric function

… are the continous counterpart to binary values.
… input are in radian unless otherwise specified (~never).

Interactive visualization of all trig functions + explanation of trig identities by gemini

Complete formulary for trigonometric functions.

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Periodicity of $\sin (ct)$

frequency = $c/2\pi$
wavelength = $2\pi /c$
→ $\sin (2\pi )$ has a period of 1, $\sin \left(2\pi /L\right)$ has a period of L

Function parameters

e.g.: $a\sin (bx+c)$
$b$ tells you how many complete periods of $\sin$ can you pack in an interval of $2\pi$:
¹
It is also called “Winkelgeschwindigkeit” / angular velocity, since you can imagine it as the green car being twice as fast as the red car → completing two circles / periods.
If b is negative, the values are mirrored along the x-axis. It is as if the car was driving backwards / in the other direction.

Notation

${\sin }^{2}x=(\sin x{)}^2=\sin (x{)}^2$

Trigonometric identities

a)

$$(x{)}^2+(y{)}^2=(1{)}^{2}s⟹{\cos }^2(\theta )+{\sin }^2(\theta )=1$$

b)

References

trigonometry
periodic function

https://aistudio.google.com/u/1/apps/drive/1L9SnwebpNLhVgMQr-Q2IKK7grUIFoxfQ?pli=1&showAssistant=true&showPreview=true&resourceKey=

Footnotes

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