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Find the value of [tex]\( s \)[/tex] in the interval [tex]\(\left[0, \frac{\pi}{2}\right]\)[/tex] that satisfies the given statement.

[tex]\(\tan s = 0.6703\)[/tex]

[tex]\(s = \square\)[/tex] radians

(Round to four decimal places as needed.)


Sagot :

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.