Why is cos -pi/6 the same as cos pi/6?

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Why is cos -pi/6 the same as cos pi/6?

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Answer 1 · 2015-05-15T07:30:14

The cosine function is even, which means that $cos(-x) = cos(x)$ .

In opposition, the sine function is odd, which means that $sin(-x) = -sin(x)$ .

You can observe that on the trigonometric circle :

enter image source here (source : http://en.wikipedia.org/wiki/Unit_circle)

You see that when you have an angle of $pi/6$ or of $-pi/6 = (11pi)/6$ , the abscissa (the $x$ position on the graph) $=$ the cosine value $= sqrt3/2$ in both cases.

In opposition, the ordinate (the $y$ position on the graph) $=$ the sine value $=1/2$ with an angle of $pi/6$ and $=-1/2$ with an angle of $-pi/6$ .

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Why is cos -pi/6 the same as cos pi/6?

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