Derivatives of Trigonometric Functions

In summary, the six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. To find their derivatives, the chain rule and the derivatives of the basic trigonometric functions are used. The derivative of the sine function is the cosine function and the purpose of finding the derivative is to understand how the function is changing at a given point, which is useful in various applications.
  • #1
DMac
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[SOLVED] Derivatives of Trigonometric Functions

I need to find the critical numbers of this function:
y = cos x - sin x where -pi <= x <= pi

I found the derivative as:

dy/dx = -(sin x + cos x)

But when I equate dy/dx to zero, I get:

sin x + cos x = 0...where do I go from here?
 
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  • #2
Well when does sinx = -cosx?
 
  • #3
Ha, lolz I can't believe I didn't think of tan x = -1. (It's getting late, and I've only had 5 hours of sleep these past two nights.) Thanks for the help. =D
 

1. What are the six basic trigonometric functions?

The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are used to describe the relationship between the sides and angles of a right triangle.

2. How do you find the derivative of a trigonometric function?

To find the derivative of a trigonometric function, you use the chain rule and the derivatives of the basic trigonometric functions. For example, the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x).

3. What is the derivative of the sine function?

The derivative of the sine function is the cosine function. This can be written as d/dx sin(x) = cos(x).

4. How do you find the derivative of a composite trigonometric function?

To find the derivative of a composite trigonometric function, you use the chain rule and the derivatives of the basic trigonometric functions. For example, the derivative of sin(2x) is 2cos(2x).

5. What is the purpose of finding the derivative of a trigonometric function?

The purpose of finding the derivative of a trigonometric function is to understand how the function is changing at a given point. This information is useful in many applications, such as physics, engineering, and economics.

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