Find the value of x satisfying the equation \(\sin^{-1}(x - 1) = \arctan(3)\).
Solution
First, calculate \(\arctan(3)\). This gives \(\arctan(3) = 1.249\) radians.
Next, we need to find \(\sin(1.249)\). Using a calculator, \(\sin(1.249) \approx 0.949\).
Set \(x - 1 = 0.949\), so \(x = 0.949 + 1 = 1.949\).
Therefore, the value of \(x\) is approximately 1.95.
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