Question

@3mar

Answer 1

(a.) State the definition of an inverse function. (b.) Explain why the sine, cosine, and tangent functions, as defined over the real numbers, do not have inverses. (c.) What do we need to do to the domain of each of these functions so that we can study their inverse behavior? (You should have a response for each of the 3 functions.)

Answer 2

I know a but not b and c

Answer 3

What is the condition to have an inverse of a function?

Answer 4

i dont know

Answer 5

It must satisfies the "horizontal line test"
http://www.mathwords.com/h/horizontal_line_test.htm

Answer 6

ok now to answer b and c @3mar

Answer 7

"b.) Explain why the sine, cosine, and tangent functions, as defined over the real numbers, do not have inverses. "

because they don't satisfy the horizontal line test. These are not one-to-one functions!

Answer 8

but the directions say we should have 3 different answers

Answer 9

????

Answer 10

wait sorry that is for part c

Answer 11

@3mar

Answer 12

Yes

Answer 13

ok so what would c be

Answer 14

"(c.) What do we need to do to the domain of each of these functions so that we can study their inverse behavior?"

What do you think?

Answer 15

I know that I usually try to help, but i honestly am stumped on this question

Answer 16

No problem, the idea is:
limit the domain of these functions in order so that they could pass the one-to-one test, i.e "horizontal line test"!!!

Answer 17

ok so what would my three responses be?

Answer 18

@3mar

Answer 19

Try for every function:sine, cosine, and tangent

Answer 20

what do ypu mean

Answer 21

What I mean is that you limit the domain of the sine function so that it would be one-to-one function!

Got it?

Answer 22

ok now what for tan and cos

Answer 23

Firstly what did you do with sine?

Answer 24

you just said
What I mean is that you limit the domain of the sine function so that it would be one-to-one function!

Answer 25

@3mar

Answer 26

Yes, so you would do this: