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Q: Is anyone of the six trigonometric functions a one to one?

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SineCosineTangentSecantCosecantCotangent

Sine Cosine Tangent ArcSine ArcCosine ArcTangent

The trigonometric functions give ratios defined by an angle. Whenever you have an angle and a side in right triangle, you can find all the other angles and sides using the six trigonometric functions and their inverses. The link below demonstrates the relationship between functions.

All six trigonometric functions can take the value 1.

sine, cosine, tangent, cosecant, secant and cotangent.

All the trigonometric functions are derived from the right angled triangle. If we consider the three sides (AB, BC, CA) of a triangle and the included angle. There is a possibility of getting six functions based on the ratios like AB/AC, BC/AC, AB/BC, BC/AB, AC/BC, AC/AB . So we will have six trigonometric functions

Six.

Not so sure about a triangel! There are, in fact 12 trigonometric functions: sine, cosine, tangent; their reciprocals, cosecant, secant and cotangent; and the inverse functions for all six: arcsine, arccosine, arctangent, arccosecant, arcsecant and accotangent. The arc functions are often written with the power -1; that is, arcsin(y) = sin-1(y).

sin(90Â°) = 1 cos(90Â°) = 0 tan(90Â°) = âˆž sec(90Â°) = âˆž csc(90Â°) = 1 cot(90Â°) = 0

sin(180) = 0 cos(180) = -1 tan(180) = 0 cosec(180) is not defined sec(180) = -1 cot(180) is not defined.

The six main trigonometric functions are sin(x)=opposite/hypotenuse cos(x)=adjacent/hypotenuse tan(x)=opposite/adjacent csc(x)=hypotenuse/opposite cot(x)=adjacent/opposite sec(x)=hypotenuse/adjacent Where hypotenuse, opposite, and adjacent correspond to the three sides of a right triangle and x corresponds to an angle in that right triangle.

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.

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