High School Calculus/Derivatives of Trigonometric Functions

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Formulas for Differentiation of Trigonometric Functions[edit]

In the following formulas the angle u is supposed to be expressed in circular measure.


Proofs[edit]

Proof for the derivative of

Let ,

then

;

therefore

;

In Trigonometry,

If we substitute and ,

we have

Hence

When approaches zero, likewise approaches zero, and as is in circular measure, the limit of

Hence


Proof for


Proof for

Since






Proof for