In Unit circle, in second quadrant, why is X taken negative?

Question

Cos theta = base / hypotenuse

Base and hypotenuse are lengths, so they should always be positive.

So why is cos 3π / 4 negative ?

Answer 1

I pinched this from another post, but it may help;

I think if you look at this animation and think about it long enough, you'll understand:

• Why circles and right-angle triangles and angles are all related
• Why sine is opposite over hypotenuse and so on
• Why cosine is simply sine but offset by $\pi/2$ radians