Final answer:
The condition number of f(x)=cos(x) is calculated by taking the absolute value of the derivative of the function and dividing it by the function itself.
Step-by-step explanation:
The condition number of a function is a measure of how sensitive the function is to changes in its input. It is calculated by taking the absolute value of the derivative of the function and dividing it by the function itself. In the case of f(x)=cos(x), the derivative is -sin(x), so the condition number can be written as | -sin(x) / cos(x) |.
Depending on the value of x, the condition number can vary.
For example, when x is close to 0, the condition number will be very large because the derivative of cos(x) is -sin(x) which is close to 0. On the other hand, when x is close to π/2 or 3π/2, the condition number will be close to 0 because the derivative of cos(x) is also close to 0.