The inverse sine is the cosecant, otherwise known as "hypotenuse over opposite" or arcsine. The cosecant is often confused as being the inverse of the cosine, which, in reality, is the secant, otherwise known as "hypotenuse over adjacent" or arccosine.
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Yes, it is called arcsin.
arc sine is the inverse function of the sine function so if y = sin(x) then x = arcsin(y) where y belongs to [-pi/2, pi/2]. It can be calculated using the Taylor series given in the link below.
To find the angle whose sine is 0.083, you can use the inverse sine function (arcsin). In degrees, this would be approximately 4.78 degrees. In radians, it is around 0.0833 radians. Since the sine function is periodic, there are additional angles in different quadrants that also satisfy this condition.
The differential of the sine function is the cosine function while the differential of the cosine function is the negative of the sine function.
Waves are periodic function, as is the sine function.