# 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 **