Why Do Negative Angles Have Opposite Trig Identities?

[Miike012]

My book was proving that..
sin(-x) = -sin(x)
tan(-x) = -tan(x)
cos(-x) = cos(x)

.. I posted an attachment of the books explanation.. I just don't understand how their explanation has anything to do with sin of a negative angle equaling sin of an angle times negative one, the same goes for tan and cos...

 

[Mark44]

Your book should have explained the sine and cosine functions in terms of the unit circle. The oddness of the sine function and the evenness of the cosine function are probably a bit easier to understand if you see the picture. See here, about the middle of the page.