# Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 130: 12

$\frac{5\pi}{4}$ radians

#### Work Step by Step

Step 1: The formula to be used here is $w=\frac{\theta}{t}$. Step 2: After substituting the values of $w$ and $t$ provided by the question into this formula, the equation becomes $\frac{\pi}{4}=\frac{\theta}{5}$ Step 3: Multiplying both sides by $5$, $\frac{\pi}{4}\times5=\frac{\theta}{5}\times5$ Step 4: Simplifying, $\theta=\frac{5\pi}{4}$ radians.

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