zbot1 said:Homework Statement
how to show using MVT that cos(cos x) is a contraction.
Homework Equations
| d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1
The Attempt at a Solution
Using that relation, the original problem is easily solved. My question is, how do we know:
| sin(cos x) sin(x) | < sin 1 ?
-zbot1
The composition of trigonometric functions is the process of combining two or more trigonometric functions to form a new function. This is done by plugging one function into another, where the output of the first function becomes the input of the second function.
Yes, trigonometric functions can be composed with non-trigonometric functions. However, the result may not always be a trigonometric function.
The mean value theorem states that for a differentiable function on an interval, there exists at least one point on the interval where the instantaneous rate of change (derivative) is equal to the average rate of change of the function over that interval.
The mean value theorem can be applied to trigonometric functions to find the average rate of change over a given interval. This can be useful in finding the maximum and minimum values of a trigonometric function.
Yes, the mean value theorem can be used to prove the existence of solutions to trigonometric equations. This is because it guarantees the existence of at least one point where the derivative of the function is equal to the average rate of change, which can help in finding solutions to equations.