Question

State the domain and range of the relation y=arccos x.

Please no direct answers. Thanks.

Answer 1

first, what is the domain/range for y=cos(x)

Answer 2

The domain is all real numbers?

Answer 3

And the range is −1 ≤ y ≤ 1...

Answer 4

yes

Answer 5

the arccos is the inverse function... the range of cos(x) will become the domain of arccos(x)

Answer 6

Okay

Answer 7

y = cos(x)

------

y = arccos(x)
cos(y) = x

inverse

Answer 8

domain and range of x = cos(y)

domain, x is -1 to 1,

Answer 9

range resulting from that domain
cos(y) = -1 at y=pi

to


cos(y)=1 at y = 0


range 0 to pi

Answer 10

you have to restrict the cosine functions domain , in order to take its inverse

cosine is not 1-to-1 function, unless you only take the restricted domain..

Answer 11

Okay, thanks

Answer 12

inverse is a reflection over line y=x, you can only do that if you take the restricted domain on cos(x) from 0 to pi/2

that is why the inverse cosine is just that one section