Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 23, 2023

Find the angle $s$ in radians that satisfies $\cos s = 0.6823$ within the interval $[0, \pi/2]$ . $\mathrm{s} = \square$ radians (round to four decimal places).

STEP 1

Assumptions1. We are given that $\cos s=0.6823$ . We are looking for the value of $s$ in the interval $\left[0, \frac{\pi}{}\right]$
3. The value of $s$ should be in radians and rounded to four decimal places

STEP 2

To find the value of $s$ that satisfies $\cos s=0.682$ , we can use the inverse cosine function, also known as arccosine.
$s = \arccos(0.682)$

STEP 3

Calculate the value of $s$ using a calculator.
$s = \arccos(0.6823) \approx0.8245$

STEP 4

Check if the calculated value of $s$ is in the given interval $\left[0, \frac{\pi}{2}\right]$ .Since $0 \leq0.824 \leq \frac{\pi}{2}$ , the value of $s$ is valid.
So, $s \approx0.824$ radians.

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