Why is $x$ in Figure 1 $x$ and not $-x$? This has caused me to not understand why $\cos(-\theta) = x$ and $\cos(\theta) = x$.
Why do opposite angles have equal cosines?
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trigonometry
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0That's just sloppy drafting of the figure. For the angles shown, the cosine is indeed negative. – 2012-04-25
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0because $x$ is the projection of the point $(x,y)$ over the X-axis, wich represent $\cos\theta$ – 2012-04-25
1 Answers
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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.
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0I 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 $-x$. – 2012-04-25
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0@Henning, you might be right. – 2012-04-25