To evaluate the given expression:
\(\sin(58°) \cdot \cos(32°) + \tan(42°) \cdot \cot(48°)\),
we first need to calculate the trigonometric values for the angles involved.
Using a calculator or trigonometric tables:
\(\sin(58°) \approx 0.8480480962\),
\(\cos(32°) \approx 0.8480480962\),
\(\tan(42°) \approx 0.9004040443\),
\(\cot(48°) \approx 1.1106125159\).
Now, substitute these values into the expression:
\(0.8480480962 \cdot 0.8480480962 + 0.9004040443 \cdot 1.1106125159\).
Calculate the individual products:
\(0.7198463080 + 0.9999999999\).
Now, add the two results:
\(0.7198463080 + 0.9999999999 \approx 1.7198463080\).
So, the evaluated value of the expression is approximately \(1.7198463080\).
The decimal expression 1.7198463080 can be rounded to 2 since the number of decimal places is quite large, and in many cases, we may only need an approximate answer. When rounding, we consider the digit right after the desired significant digit (in this case, the digit after the "1"):
1.7198463080≈2
So, for practical purposes and rounding to the nearest whole number, the evaluated expression can be approximated as 2.
