Question

Inverse trig function question?

Answer 1

Here is the problem I'm working on. For part 1, I think I sketched it correctly but it was really tiny?

For Part II, I put all real numbers for the domain and [-1, 1] for the range.

I'm stumped on part III.

Answer 2

I don't see your sketch. Did you sketch it by hand?

Answer 3

Yes, I did. I'll take a picture of it

Answer 4

`For Part II, I put all real numbers for the domain and [-1, 1] for the range.`
correct on both

Answer 5

Here is my graph

Answer 6

That looks good.

Answer 7

for part III, you will restrict the domain in such a way that the function is one-to-one (i.e. it passes the horizontal line test). Then reflect it over the line y = x to get the inverse function

Answer 8

So I should restrict it to one full period? would [0, 2pi] work?

Answer 9

No it would not. You can pass a horizontal line through more than one point (if you just focus on the interval from 0 to 2pi)

Answer 10

hmmm. how would I restrict the domain then?

Answer 11

[0, pi] ?

Answer 12

why not 0 to pi?

yes

Answer 13

which is represented by the green shaded region
https://www.desmos.com/calculator/gk2vz4gpaf

Answer 14

Awesome! Now to reflect that over the line y = x, I switch the x and y coordinates correct?

Answer 15

correct

Answer 16

what would the sketch look like?

Answer 17

This?

Answer 18

Why are the axis so big? lol

Answer 19

It looks good.

https://www.desmos.com/calculator/qfafcyrled

Type `y = arccos(x)` into the input box to have desmos graph the inverse function. Just as a way to check.

Answer 20

on your paper? or on desmos?

Answer 21

On the paper :P

Answer 22

Just unfortunate scaling

Answer 23

Hah. Okay. Thanks a bunch!

Answer 24

You're welcome