Inverse trig functions q (1 Viewer)

[ataratar]

Hey guys - would really appreciate it if someone could help me out. Show graphically that (inverse)cos(x) + (inverse)cos(-x) = pie.
Thankyaa

 

[Carrotsticks]

Do you know the following:

- Given f(x), draw f(-x)

- How to sketch y = inverse cos (x)

- How to add functions (or ordinates).

Pie =)

 

[ataratar]

yes I know how to do the first two but not how to add functions. I sketched inversecos(x) and inverse cos(-x) but they are just a reflection of each other about the y axis so i don't understand how they equal pie when added together - and I don't think adding functions is in the course

 

[Cleavage]

Complete using this method;



Work on LHS, to prove LHS = RHS

EDIT: Did not read graphically part

 

[youngsky]

From these 2 graphs, pick any x co-ordinate, e.g.

Let x = 1, graphically, you can see that:
at x = 1 on y = arccos(x), y = 0
at x = 1 on y = arccos(-x), y = π
add these two y values and you get π.

Do this for any x co-ordinate in the domain and you will get π.

Algebraically:

= arccos(x) + arccos(-x)
As arccos = π - arccos(x) using this trig identity,
= arccos(x) + π - arccos(x)
= π

 

[braintic]

In words:

On the graph of arccos x, pick a positive number x.
You should be able to see by symmetry that arccos(-x) is greater than pi/2 by the same amount that arccos(x) is less than pi/2.
Call these numbers p/2 + c and pi/2 - c if you like.

When you add these expressions, you get pi.