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This is going to require some visualization. Cosine is defined as the x-value on the unit circle.

If you picture where a point would be, for example, at the angle of pi/6 (30°) you get a coordinate of (√(3)/2 , 1/2) so cosine is √(3)/2 and sine is 1/2

To find a negative angle you take the reflection across the x-axis. Since this does not chance the x-value, only the y, cosine does not change. The coordinates of -(pi/6) (-30°) are (√(3)/2 , -1/2).

cos(-x) = cos(x)

sin(-x) = - sin(x)■

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Q: Why does cosine x equal cosine negative x?
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