Derivative of trigonometric functions

When we have trigonometric functions, the derivatives are all related to the trigonometric identities. Let's plot sine, cosine and tangent on the same space:

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Notice that close to the origin the tangent almost coincides with the sine. The rate of change of both functions invert its sign at the origin. The point where the sine is max is also the point where cosine is zero. The opposite is also true, where the cosine is max the sine is zero. The point where cosine and sine intercept each other is the angle [math]\displaystyle{ \pi / 4 }[/math] in the unit circle.