Problem

Find a value of $\mathrm{s}$ in the interval $\left[0, \frac{\pi}{2}\right]$ that satisfies the given statement.
\[
\csc s=1.4261
\]

Answer

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Answer

Final Answer: The value of \(s\) that satisfies the given statement is \(\boxed{0.777}\) radians or \(\boxed{44.524}\) degrees

Steps

Step 1 :Given that \(\csc s = 1.4261\)

Step 2 :We know that \(\csc s\) is the reciprocal of \(\sin s\), so \(\sin s = \frac{1}{\csc s} = \frac{1}{1.4261} = 0.701213098660683\)

Step 3 :We can find the value of \(s\) by taking the arcsine of \(\sin s\), so \(s = \arcsin(0.701213098660683) = 0.7770975918659346\) radians

Step 4 :We can also convert this to degrees by multiplying by \(\frac{180}{\pi}\), so \(s = 0.7770975918659346 \times \frac{180}{\pi} = 44.52441228369783\) degrees

Step 5 :Final Answer: The value of \(s\) that satisfies the given statement is \(\boxed{0.777}\) radians or \(\boxed{44.524}\) degrees

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