Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Trig Trig Trig

Consider the function $f(x)=\cos(\sin(\cos(x)))$, with $x$ measured in radians.

What turning points can you find?

What are the maximum and minimum values of the function?

## You may also like

### A Close Match

Or search by topic

Age 16 to 18

ShortChallenge Level

- Problem
- Solutions

Consider the function $f(x)=\cos(\sin(\cos(x)))$, with $x$ measured in radians.

What turning points can you find?

What are the maximum and minimum values of the function?

Did you know ... ?

This function is bounded, continuous and differentiable at all points. Mathematicians often use knowledge of conditions such as these to deduce lots of information about the properties of functions without the need for extensive calculation. In first year undergraduate analysis courses theorems are rigorously stated and proved which support intuitive statements such as 'between any two maxima a minimum must be found if the function is finite, continuous and differentiable'.

This function is bounded, continuous and differentiable at all points. Mathematicians often use knowledge of conditions such as these to deduce lots of information about the properties of functions without the need for extensive calculation. In first year undergraduate analysis courses theorems are rigorously stated and proved which support intuitive statements such as 'between any two maxima a minimum must be found if the function is finite, continuous and differentiable'.

Can you massage the parameters of these curves to make them match as closely as possible?