Exploring the Value of cos^(-1)(1): Understanding the Inverse Cosine Function and Its Restricted Range

cos^-1(1)

To find the value of cos^(-1)(1), let’s first understand what this expression means

To find the value of cos^(-1)(1), let’s first understand what this expression means.

The notation cos^(-1)(x) represents the inverse cosine function, sometimes also denoted as arccos or acos. It is the inverse function of the cosine function, which means it gives you the angle whose cosine is equal to x.

In this case, we have cos^(-1)(1). This means we are looking for the angle whose cosine is equal to 1.

To find this angle, we can recall the unit circle. The unit circle is a circle with a radius of 1, centered at the origin (0,0) of a coordinate plane.

At the point (1,0) on the unit circle, the angle formed with the positive x-axis is 0 degrees or 0 radians. At this point, the x-coordinate is 1, and the cosine of 0 degrees or 0 radians is indeed equal to 1.

Since the cosine function has a period of 360 degrees or 2π radians, the values of cosine repeat after each full revolution around the unit circle. Therefore, there are infinitely many angles whose cosine is equal to 1.

So, cos^(-1)(1) is equal to 0 degrees or 0 radians, and all other angles that are coterminal with 0 degrees or 0 radians such as 360 degrees, -360 degrees, 720 degrees, -720 degrees, etc.

It’s important to note that the inverse cosine function has a restricted range of [0,π]. This means that when using the inverse cosine function, the output will be an angle between 0 degrees and 180 degrees (or between 0 radians and π radians).

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