Find the Exact Value arccos(-0.546)

Problem

arccos(−0.546)

Solution

1. Identify the inverse trigonometric function and its argument. We are looking for an angle θ in the interval [0,π] such that cos(θ)=−0.546

2. Recognize that −0.546 is not a standard value from the unit circle (like 0.5 or √(,3)/2, so the exact value is expressed as the inverse cosine of the given decimal.

3. Determine the quadrant of the angle. Since the cosine value is negative and the range of arccos(x) is [0,π] the angle must be in the second quadrant (between π/2 and π.

4. Calculate the numerical value using a calculator if a decimal approximation is required, ensuring the calculator is in the desired mode (radians or degrees).

Final Answer

arccos(−0.546)≈2.1486* radians

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