sin

A function that can be used in Formulas.

Syntax and semantics

sin (x)
compute the sine of x.
    Axes: -5, 5, -1.1, 1.1
     Draw inner box
     Draw function: -5, 5, 1000, ~ sin (x)
     One mark bottom: -3*pi/2, "no", "yes", "yes", "\-m3%\pi/2"
     One mark bottom: -pi, "no", "yes", "yes", "\-m%\pi"
     One mark bottom: -pi/2, "no", "yes", "yes", "\-m%\pi/2"
     One mark bottom: 0, "no", "yes", "yes", "0"
     One mark bottom: pi/2, "no", "yes", "yes", "+%\pi/2"
     One mark bottom: pi, "no", "yes", "yes", "+%\pi"
     One mark bottom: 3*pi/2, "no", "yes", "yes", "+3%\pi/2"
     One mark left: -1, "no", "yes", "yes", "\-m1"
     One mark left: 0, "no", "yes", "yes", "0"
     One mark left: 1, "no", "yes", "yes", "+1"
     Text bottom: "yes", "%x \->"
     Text left: "yes", "##sin# (%x)"
     Text top: "no", "##just over one and a half periods of a sine wave"

This picture illustrates the following properties of the sine function:

• sin (x) is zero for all values of x that are integer multiples of π.
• The extrema of sin (x) are −1 and +1.
• sin (x) is −1 or +1 wherever x is an odd multiple of π/2.
• The function is periodic with period 2π, i.e., sin (x+2π) = sin (x).
• The function is symmetric around π/2, i.e. sin (π/2−x) = sin (x).
• The function is antisymmetric around 0, i.e. sin (−x) = − sin (x); in other words, if you take the sine curve and rotate it by 180 degrees around the origin (i.e. the point (0, 0)), then you get the same curve again.

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© Paul Boersma 2023