Confusion in basic trigonometry

Question

We know when $\theta$ is acute, cos $\theta$ is positive. However in the above diagram, the adjacent side is negative and hence cos $\theta$ should be negative. This is obviously incorrect. Where am I wrong?

Answer 1

For convention angles are misured from positive x axis counterclockwise direction.

https://en.wikipedia.org/wiki/Unit_circle

Answer 2

In the end, this boils down to the fact that $\cos(\theta)$ does not depend on how you draw $\theta$.

That said, depending on the problem you'd like to solve, the correct angle to consider might be $\pi - \theta$, rather than $\theta$.

Answer 3

Contrary to your thinking, but using your own terms, the adjacent side is positive. Because you are counting the angles from the positive side.

In the figure, the right side of the $x$ axis plays no role (other than misleading you).