f(x) = cos^-1 x
f'(x) = -1/√(1 – x^2)
The function f(x) = cos^-1(x), where x is a value between -1 and 1, is the inverse of the cosine function, cos(x).
To find the value of f(x) for a given x, we need to determine the angle whose cosine is x. For example, if x = 0.5, then f(x) = cos^-1(0.5), which means we need to find the angle whose cosine is 0.5.
We can use a calculator to find this angle, by calculating the inverse cosine of 0.5. The result is approximately 60 degrees (or pi/3 radians). Therefore, f(0.5) = 60 degrees (or pi/3 radians).
Similarly, we can find f(x) for other values of x between -1 and 1 using the same method. However, it’s important to note that the domain of the function is restricted to [-1, 1], since the inverse cosine function is only defined for values of x between -1 and 1.
Another important feature of the function f(x) = cos^-1(x) is that its range is also restricted to [0, pi]. This means that the output of the function is always a value between 0 and pi radians (or 0 and 180 degrees).
Overall, understanding inverse trigonometric functions requires a solid understanding of trigonometry and the unit circle. It’s important to approach these functions with caution and careful attention to their domain and range restrictions.
More Answers:
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