Question

MEDAL!! True or False: For a trigonometric function, y =f(x), then x=F^-1(y). Explain your answer.

Answer 1

false

Answer 2

Trig functions are periodic. Consider this example:\[\rm Statement~1:\sin(0) = 1\]\[\rm Statement 2: \sin^{-1}{(1)} = 0\]The first statement is true. But what I want to focus on is the second. Since \(2\pi\) also returns 0, why is that not the inverse function? So clearly, claiming that the sine inverse of 1 is not 0.

What does this mean? If \(\sin(x) = y\) then is it accurate to say \(\sin^{-1}(y) = x\)? In the above example, we have taken \(x \) to be \(0\) and \(y\) to be \(1\).

Answer 3

So what are your thoughts on this?

Answer 4

so answer is false because they are not inverses of each other even though they appear that way at first.

Answer 5

Exactly. Rather, 0 is not the only inverse.

Answer 6

So right.

Answer 7

Ok, thank you! I have a few more like these, so hopefully you can help

Answer 8

hope so