Radian Measure Quiz: Test Your Knowledge with Answers

📚 Quick Study Guide

• 📐 Definition: Radian measure is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
• 🔄 Conversion: To convert from degrees to radians, multiply by $\frac{\pi}{180}$.
• 🔢 Formula: Radians = Degrees $\times \frac{\pi}{180}$
• 🥧 Key Values: $180^{\circ} = \pi$ radians, $360^{\circ} = 2\pi$ radians, $90^{\circ} = \frac{\pi}{2}$ radians.
• 🔗 Arc Length: The arc length ($s$) of a circle is given by $s = r\theta$, where $r$ is the radius and $\theta$ is the angle in radians.
• 🧮 Angular Velocity: Angular velocity ($\omega$) is the rate of change of angular displacement: $\omega = \frac{\theta}{t}$, where $\theta$ is in radians and $t$ is time.

🧪 Practice Quiz

1. What is the radian equivalent of $60^{\circ}$?
   1. $\frac{\pi}{6}$
   2. $\frac{\pi}{4}$
   3. $\frac{\pi}{3}$
   4. $\frac{\pi}{2}$
2. Convert $\frac{3\pi}{4}$ radians to degrees.
   1. $120^{\circ}$
   2. $135^{\circ}$
   3. $150^{\circ}$
   4. $270^{\circ}$
3. An arc of length 10 cm subtends an angle of 2 radians at the center of a circle. What is the radius of the circle?
   1. 2 cm
   2. 5 cm
   3. 10 cm
   4. 20 cm
4. A wheel is rotating at an angular velocity of $4\pi$ radians per second. How many complete revolutions does it make in 10 seconds?
   1. 5
   2. 10
   3. 20
   4. 40
5. What is the radian equivalent of $270^{\circ}$?
   1. $\frac{\pi}{2}$
   2. $\pi$
   3. $\frac{3\pi}{2}$
   4. $2\pi$
6. Convert $\frac{5\pi}{6}$ radians to degrees.
   1. $120^{\circ}$
   2. $150^{\circ}$
   3. $210^{\circ}$
   4. $300^{\circ}$
7. If the radius of a circle is 6 cm and the arc length is $3\pi$ cm, what is the angle subtended at the center in radians?
   1. $\frac{\pi}{6}$
   2. $\frac{\pi}{3}$
   3. $\frac{\pi}{2}$
   4. $\pi$