Question

The expression cos^-1(3/5) has an infinite number of values. True or False?

Please explain. Thank you!

Answer 1

We need to be careful!
The answer is false. Here's why.

With a capital letter, Cos^-1 (3/5) has exactly one solution, between 0 and 180 degrees inclusive. Cos^(-1) is a function.

On the other hand, with a lower case letter, cos^-1 (3/5) has infinitely many values. In fact, cos^(-1) is nowhere near being a function.
(All of its values are given by Cos^(-1)(3/5) + 2 pi n and -Cos^(-1)(3/5) + 2 pi n for any integer n.)

Answer 2

Fan and medal?! Thx

Answer 3

In order for y=cos(x) has to to be defined on a interval such that y=cos(x) is one-to-one.
So if we define y=cos(x) on the interval from x=0 to x=pi, then we have a function that is one-to-one.
That means for each x in the restricted domain will have a y value different from any other x.
So if we look at y=arccos(x) then we know we are getting one y for each x since we were getting one x for each y for the y=cos(x) on the interval [0,pi]

Answer 4

Ok thank you for the explanation I understand a little better now.