Explain why the smallest possible value of cosine is -1

Question

anonymous · Answer

Is this a trick question? I thought the domain of cosine was all real numbers?

phi · Answer

this is asking about the range of the cosine function

anonymous · Answer

but if i put cos = -2 in calculator, it still comes up with a similar answer as, for example, cosine of -.5 ... Don't get it... shouldn't the calculator reflect this?

phi · Answer

The question is asking   what is the smallest value you get for cos(x)
In other words, if you try all possible values for x, what is the smallest number you will get from cos(x)

phi · Answer

See http://www.google.com/search?client=safari&rls=en&q=cos(x)&ie=UTF-8&oe=UTF-8

anonymous · Answer

Thanks, now just give me 10 minutes to fully understand..

anonymous · Answer

whoa... this is amazing... thanks

anonymous · Answer

I'm going to make some flash cards... I appreciate your help, phi.