Learning Resources

Focus K: Finding q from a Point (cos q, sin q)

It is very important that you not confuse the notation used for inverse functions. You should be familiar with the "f of x" notation to represent a function, e.g.
f(x) = 2x + 1; g(x) = x²,  p(x) = sin(x), etc.

The notation used for the inverse of a function written in the "f of x" notation is f^-1(x); g^-1(x); sin^-1(x), etc. The -1 superscript is NOT AN EXPONENT. It does not mean take the reciprocal of the function. Instead, it indicates finding the inverse of the function and it should be read that way. Thus, f^-1(x) is read as "the inverse of function f" and sin^-1(x) is read as "the inverse of  sin (x)".

On your TI83 calculator, pressing the [2nd] button followed by pressing the [sin] button gives the inverse of the sine function. Note the symbol used on the calculator to denote this [2nd] function. It is sin^-1 . It is not the reciprocal of sine. Try an example to make sure you understand this. Use your calculator to find sin (63°). Using the value you thus obtained, find sin^-1 of the value (the inverse function) and 1/value (the reciprocal).

In the case of the trigonometric functions, the inverse functions have other specialized names that you will see used in other courses, especially in post secondary courses. Although we do not use the terms in this course, you should be aware that the expression used to denote the inverse sine or sin^-1 is the arcsin, to denote cos^-1 is arccos, and to denote tan^-1 is arctan.