The general equation of the sinusoid is [tex]f(x)=sinx[/tex]
"A sine wave or sinusoidal is a continuous or mathematical curve which is used to describe a smooth periodic oscillation."
We know,
A Sinusoidal function is a function that can be modelled using a sine wave.
The sine graph repeats itself after a period of 2π, which shows the function is periodic with a period of 2π.
f (x) = sin x and f (x) = cos x are similar apart from a phase shift, both functions are sinusoidal.
f (x) = tan x is a trigonometric function, but its graph is completely different.
The graph of a sinusoidal function is a smooth periodic graph.
The graph is continuous all over the x-axis and also it repeats itself after every fixed interval.
∵ A phase shift is the only difference between sine and cosine, any sinusoidal function that can be modelled using sine can also be modelled using cosine.
The general sinusoidal function is [tex]f(x)=[/tex]±[tex]a.sin(b(x+c))+d[/tex]
Where as,
± controls the reflection across the x - axis, coefficient a controls the amplitude , constant d controls the vertical shift, coefficient b controls the horizontal stretch.
∴ The general equation of the sinusoid is [tex]f(x)=sin x[/tex]
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