f(x) = cos x
f'(x) = -sin x
Function f(x) = cos x is a trigonometric function which represents the cosine of x, where x is the angle measured in radians.
Some important characteristics of this function are:
1. Domain: The domain of the function is all real numbers. In other words, we can input any value for x and the function will return a value between -1 and 1.
2. Range: The range of the function is between -1 and 1. This means that the function output will always be within this range.
3. Periodicity: The function is periodic with a period of 2π. This means that if we add any integer multiple of 2π to x, the function value will remain the same.
4. Even function: The function is an even function, which means that f(x) = f(-x) for any value of x. This results in a symmetry with respect to the y-axis.
5. Continuous function: The function is continuous at all points in its domain. This means that there are no sudden jumps or breaks in the plot of the function.
Some common applications of cosine function include:
1. Signal processing and electronics.
2. Heat transfer and fluid mechanics.
3. Astronomy and celestial mechanics.
4. Vibrations and oscillations.
5. Music theory and sound engineering.
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