Discovering The Domain And Range Of Cos⁻¹(X) – A Comprehensive Guide.

The domain of cos−1(x) is__________and the range is__________

[−1,1]; [0,π]

The domain of cos⁻¹(x) is -1≤x≤1 because the range of cosine function is [-1, 1] and the inverse cosine function is defined only for values within this interval.

The range of cos⁻¹(x) is 0° ≤ cos⁻¹(x) ≤ 180° (or 0 ≤ cos⁻¹(x) ≤ π in radians). This is because cos⁻¹(x) gives the angle for which the cosine is equal to x. The cosine function has a maximum value of 1 and a minimum value of -1, so the range of angles for which the cosine is equal to x is from 0 to 180 degrees (or 0 to π radians).

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