cos^(-1)x or arccos(x)
The expression cos^(-1)x or arccos(x) represents the inverse cosine function
The expression cos^(-1)x or arccos(x) represents the inverse cosine function. It is the trigonometric function that gives the angle whose cosine is equal to x.
To understand this concept better, let’s consider a right triangle. In a right triangle, the cosine of an angle is defined as the length of the adjacent side divided by the hypotenuse. So, if the cosine of an angle is x, we can say that cos(angle) = x.
By taking the inverse cosine or arccosine of x, we are finding the angle whose cosine is equal to x. In other words, cos^(-1)x or arccos(x) will provide the angle θ such that cos(θ) = x.
The arccosine function has a specific range to ensure unique values. It takes input in the range -1 ≤ x ≤ 1 because the cosine of an angle will always be within that range. The output of arccosine will be an angle in radians between 0 and π (or in degrees between 0° and 180°), representing the principal value of the angle.
For example, if we evaluate arccos(0.5), we are finding the angle θ such that cos(θ) = 0.5. The result would be π/3 (or approximately 60°) since the cosine of 60 degrees is 0.5.
Overall, the arccosine function is used to find angles when the cosine value is known, helping us to solve various trigonometric problems involving angles.
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