The range of the circular trig functions sin and cos is is [-1,1], but even in the case of circular functions the range of the tangent function is all real numbers. This is of course true of tangent even if we do not limit it to circular functions. So your question, I assume, is asking about all trig functions. If so the range is all real numbers.
circular, smooth,
Sine, Cosine, Tangent, Cotangent, secant and cosecant
In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic. Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos. Tangent is the third basic ratio defined as Sin/Cos. For each of these three, there is a corresponding reciprocal function: Sine -> Cosecant (cosec or csc) Cosine -> Secant (sec) Tangent -> Cotangent (cot). Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1. The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.
Yes. The cosine function is continuous. The sine function is also continuous. The tangent function, however, is not continuous.
An inverse is NOT called a circular function. Only inverse functions that are circular functions are called circular functions for obvious reasons.
importance of circular function
"Circular functions" is basically another name for "trigonometric functions".
They are the sensory organs for balance.
The function of semi circular canal in the ear is balance and orientation
circular shape in the outer ear
*it enables the circular flow of economy
Please check the help files of the matlab circular convolution . Matlab already has a readymade function for it.
The two facial muscles that are circular are the Orbicularis Oculi(around eye), and the Orbicularis Oris(around mouth).
Circular muscles help in extension and narrowing of the body of the earthworm. When circular muscles contract the protractor muscles relax causing the retractor muscles to contract, thus withdrawing the setae.
A circular band of muscle that contracts and relaxes to make the pupil larger or smaller .
Sin (0) isn't a function, it's a number.