Find the Exact Value arccos(0.56)

Problem

arccos(0.56)

Solution

1. Identify the given value as a decimal and convert it to a fraction to see if it corresponds to a known unit circle value.

0.56=56/100

2. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4.

56/100=14/25

3. Evaluate the expression using the inverse cosine function. Since 14/25 is not a standard value from the unit circle (like 0 0.5 or √(,3)/2, the exact value is expressed as the inverse trigonometric function itself.

arccos(0.56)=arccos(14/25)

Final Answer

arccos(0.56)=arccos(14/25)

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