Remember these derivatives of the trigonometric functions:
Differentiation of sin(x) and cos(x)
To begin with, we know that differentiation is a method to find the gradient of a curve.
Rule of differentiation is if , then . However in this article we will focus entirely on differentiation of trigonometric functions.
Consider the graph of in the range . We draw tangents to the sin curve at the points where radians.
We now plot the values of the gradients of these tangents and we obtain a graph of cos(x). As shown in Fig 2.
Hence, this shows that derivative of sin(x) is cos(x). It can be written as:
when x in radians.
Similarly, we can find that:
Differentiation of tan(x)
Let’s assume ,
using quotient rule
Differentiation of sec(x)
Let’s assume: ,
Differentiation of cosec(x)
Taking the derivative:
Hence, to conclude derivatives of trigonometric functions are:
Q. Differentiate with respect to x
use the identity