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Here is the problem: Find arccos(0.25) and every angle in [0°, 360°) with cos x equals 0.25.

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Find the angle whose cos is 0.25: the principal value of arccos, every solution of cos(x) equals 0.25 in one turn, and the general solution.

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Principal value of arccos, taken in the range [0, pi]. The value is not one of the standard exact values, so the angle is given as a decimal.

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Cosine is even, so x and negative x (that is, 360° minus x) give the same value.

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Solutions in one full turn, 0° less than or equal to x less than 360°.

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General solution, n any integer.

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So the answer is arccos(0.25) equals 75.52248781° (1.318116072 rad); solutions in [0°, 360°): 75.52248781°, 284.4775122°; general: x equals plus or minus 75.52248781° plus 360°n.

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An inverse trigonometric function returns one angle, the principal value. Because the trigonometric functions repeat, the equation cos(x) equals 0.25 has infinitely many solutions; the calculator lists those in one turn and the general pattern.

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Substituting each solution back: cos(75.52248781°) approximately 0.25; cos(284.4775122°) approximately 0.25.