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- Thread starter Elissa89
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- Apr 4, 2014

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A conjecture is something that you think might be true.I don't even know what a conjecture is

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

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 $y=cos(x)$

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- Mar 1, 2012

- 642

https://en.wikipedia.org/wiki/ConjectureI don't even know what a conjecture is

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

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.