To determine the value of [tex]\( s \)[/tex] in the interval [tex]\([0, \frac{\pi}{2}]\)[/tex] that satisfies the equation [tex]\( \tan s = 0.6703 \)[/tex], we need to follow these steps:
1. Understand the equation: The given equation is [tex]\(\tan s = 0.6703\)[/tex]. Here, the tangent of [tex]\( s \)[/tex] is given as 0.6703.
2. Find the inverse function: To isolate [tex]\( s \)[/tex], we need to apply the inverse tangent (arctangent) function. The arctangent function, denoted as [tex]\(\tan^{-1}\)[/tex] or [tex]\( \arctan \)[/tex], will give us the angle whose tangent is 0.6703.
3. Compute the angle: By applying the inverse tangent function to 0.6703, we get:
[tex]\[
s = \arctan(0.6703)
\][/tex]
4. Round the result: Evaluating the inverse tangent of 0.6703, we find that:
[tex]\[
s \approx 0.590513771839581 \, \text{radians}
\][/tex]
To provide a rounded answer accurate to four decimal places:
[tex]\[
s \approx 0.5905 \, \text{radians}
\][/tex]
Therefore, the value of [tex]\( s \)[/tex] in the interval [tex]\([0, \frac{\pi}{2}]\)[/tex] that satisfies [tex]\( \tan s = 0.6703 \)[/tex] is [tex]\( \boxed{0.5905} \)[/tex] radians.
