The graph of sine is the curve
consisting of all the points \(\bigl(x, \sin(x)\bigr)\) in the plane.
The graph of cosine is defined similarly.
A curve that is based on the graph of sine or cosine
is called a sinusoidal curve.
Sine and cosine are periodic functions,
with a period of \(360°.\)
I.e. for any integer \(n\) we have
\(\sin(x) = \sin(x + 360°) = \dotsb = \sin(x + 360° n).\)
The amplitude of a sinusoidal curve
is its maximal change in height from its midline;
sine has a default amplitude of one.
The phase shift of a sinusoidal is the horizontal shift
of the curve away from its parent sine/cosine graph.
Altogether, the graph of
\(a\sin\bigl(k(x-b)\bigr) + v\)
will have period \(\frac{360°}{k},\)
amplitude \(|a|,\)
and phase shift \(b.\)
It will be shifted upwards by \(v\)
but we have no vocab term for that.
Secant and cosecant also have period of \(360°.\)
Tangent and cotangent however have a period of \(180°.\)
The graphs of these functions have vertical asymptotes
at the holes in their domain.
