Uncovering the Mystery of cos(-pi)=-1: Insights and Explanations

[SMA_01]

Sorry I made a mistake in the title, I was thinking of something else I meant "Why is cos(-pi)=-1?"

cos(-pi)=-1, why is this so? I feel like maybe I'm missing the obvious, but I would think that it's equal to 1, considering cos(pi)=-1?

 

[Petek]

The cosine function satisfies the identity

cos (-x) = cos (x).

Perhaps you are thinking of the sine function? It satisfies the identity

sin (-x) = -sin (x).

 

[SMA_01]

@Petek: Wow I feel slow, totally passed me that cosine is an even function lol. Thanks

 

[SammyS]

Think about the unit circle !

Where is the angle π relative to the angle -π ?

 

[QuarkCharmer]

As pointed out above, cosine is an even function.

Another way to think about it is that the period of cosine is 2π. So if cos(m)=A
Then cos(k2π+m) = A, where k is some integer. In your case, you say that cos(π) = -1, so it must be true that cos(π - 2π) = -1, ie: cos(-π) = -1