# graph the function y=-1/2[cos(x+pi)+cos(x-pi)] and make a conjecture

#### Elissa89

##### Member
I don't even know what a conjecture is

y=-1/2[cos(x+pi)+cos(x-pi)]

#### DavidCampen

##### Member
I don't even know what a conjecture is

y=-1/2[cos(x+pi)+cos(x-pi)]
A conjecture is something that you think might be true.

We know that $cos(x+\pi)$ = $cos(x-\pi)$
so $y=-\frac{1}{2}[2cos(x+\pi)] = -cos(x+\pi)$
also, since we know that $cos(x+\pi) = -cos(x)$ we would have $y=cos(x)$

so maybe that is supposed to be the conjecture, that $y=cos(x)$

Last edited:

#### skeeter

##### Well-known member
MHB Math Helper
I don't even know what a conjecture is

y=-1/2[cos(x+pi)+cos(x-pi)]
https://en.wikipedia.org/wiki/Conjecture

The directions in the title of your post say to graph the function and make a conjecture based on what you see in the graph.

Note the graph of $y$ shows the basic cosine curve reflected over the x-axis ... in other words, one could make a conjecture that $y=-\cos{x}$.

David went a step further and proved the conjecture using basic identities.