On-line Math 21

3.1  Trigonometric functions

3.1.1  Derivatives of sin(x)\protect and cos(x)\protect .

The derivative of sinx\protect .

The derivative of the sine function sin(x) (or sinx ) is the first derivative you can't figure out from the definition just using enough algebra to cancel a power of h top and bottom. However, what it does take is the trigonometric limits we just derived.

Theorem 1 The functions sinx and cosx have the following derivatives:

(sinx)¢ = cosx (cosx)¢ = -sinx

Example 2 Find (tanx)¢.

Solution

Example 3 Find (secx)¢.

Solution

Exercise 4 Find (cotx)¢.

This is similar to the previous ones. Watch for signs ( ±).

Exercise 5 Find (cscx)¢.

Example 1 Find (x³cosx)¢.

Solution

Exercise 6 Find (sinxcosx)¢.

Example 1 Find the tangent line to the curve y = sin(x) at (p/6,1/2) , and use that to find, approximately, sin(p/6+0.1) .

Solution

Copyright (c) 2000 by David L. Johnson.