Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Why is $x$ in Figure 1 $x$ and not $-x$? This has caused me to not understand why $\cos(-\theta) = x$ and $\cos(\theta) = x$.

share|cite|improve this question
That's just sloppy drafting of the figure. For the angles shown, the cosine is indeed negative. – Henning Makholm Apr 25 '12 at 1:12
because $x$ is the projection of the point $(x,y)$ over the X-axis, wich represent $\cos\theta$ – Abdelmajid Khadari Apr 25 '12 at 1:12
up vote 0 down vote accepted

The point has co-ordinates $(x,y)$. In the diagram, $x$ is a negative number, but that's OK - variables are allowed to stand for negative numbers. The angle $\theta$ is in the second quadrant, where the cosine function is negative, so $\cos\theta=x$ is perfectly consistent.

share|cite|improve this answer
I understood the OP's problem as being that the diagram seems to claim that the length of the line segment between the origin and $(\cos\theta,0)$ is $x$ -- but actually it is $|x|$, which in this case equals $-x$. – Henning Makholm Apr 25 '12 at 10:30
@Henning, you might be right. – Gerry Myerson Apr 25 '12 at 10:58

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.