Confused again:( help?

Question

The six trigonometric functions are not invertible. What has to be done to make them invertible

Answer 1

To make the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) invertible, we need to restrict their domains to certain intervals where they are one-to-one (i.e., have a unique inverse function).

One common way to do this is to restrict the domains of the trigonometric functions to intervals of size π or 2π, where they have a single maximum and minimum value. By defining new functions called inverse trigonometric functions, they are as follows:

arcsin(x) or sin^-1(x) for the inverse sine function, which is defined on the interval [-π/2, π/2].

arccos(x) or cos^-1(x) for the inverse cosine function, which is defined on the interval [0, π].

arctan(x) or tan^-1(x) for the inverse tangent function, which is defined on the interval [-π/2, π/2].

arccot(x) or cot^-1(x) for the inverse cotangent function, which is defined on the interval [0, π].

arcsec(x) or sec^-1(x) for the inverse secant function, which is defined on the interval [0, π/2] ∪ [π/2, π].

arccsc(x) or csc^-1(x) for the inverse cosecant function, which is defined on the interval [-π/2, 0] ∪ [0, π/2].

Hope this helps!