Problem

Use the formula $\omega=\frac{\theta}{t}$ to find the value of the missing variable.
\[
\theta=\frac{3 \pi}{4} \text { radians, } t=5 \mathrm{sec}
\]
$\omega=$ radians per sec
(Simplify your answer. Type an exact answer, using $\pi$ as needed.)

Answer

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Answer

Final Answer: \(\boxed{0.471}\) radians per sec.

Steps

Step 1 :Given that the angle \(\theta\) is \(\frac{3 \pi}{4}\) radians and the time \(t\) is 5 seconds, we can find the angular velocity \(\omega\) using the formula \(\omega=\frac{\theta}{t}\).

Step 2 :Substitute the given values into the formula: \(\omega=\frac{\frac{3 \pi}{4}}{5}\).

Step 3 :Simplify the expression to find the value of \(\omega\).

Step 4 :Final Answer: \(\boxed{0.471}\) radians per sec.

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