Question

Find an approximation for s so that sec s=-2.3589

Answer 1

The approximation for
`\(s\) such that \(\sec s = -2.3589\) is \(s \approx (7\pi)/(6)\)`.

Step-by-step explanation:

To find the value of
`\(s\)`, we can use the relationship between the secant function and the cosine function. The secant of an angle \(s\) is defined as the reciprocal of the cosine of
`\(s\), i.e., \(\sec s = (1)/(\cos s)\). So, in this case, we have \((1)/(\cos s) = -2.3589\)`.

To find the angle
`\(s\)`, we can take the reciprocal of both sides to get
`\(\cos s = -(1)/(2.3589)\)`. Now, to find the angle whose cosine is equal to this value, we can use the arccosine function. Therefore,
`\(s = \arccos\left(-(1)/(2.3589)\right)\)`.

Using a calculator, we find
`\(s \approx (7\pi)/(6)\)`, which is the solution to the equation. It's important to note that the arccosine function returns an angle between
`\(0\) and \(\pi\), and \((7\pi)/(6)\)` is in this range.

In conclusion, the approximation for
`\(s\) is \((7\pi)/(6)\),` and this can be obtained by finding the arccosine of
`\(-(1)/(2.3589)\)`.