The image shows a math problem that asks to:

"Convert 150° into radians and $\frac{\pi}{4}$ into degrees."

1. Convert 150° into radians:

We use the formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$ So for 150°: $150° \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} \text{ radians}$

2. Convert $\frac{\pi}{4}$ radians into degrees:

To convert radians to degrees, we use the formula: $\text{Degrees} = \text{Radians} \times \frac{180}{\pi}$ So for $\frac{\pi}{4}$: $\frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45°$

Summary:

• 150° = $\frac{5\pi}{6}$ radians
• $\frac{\pi}{4}$ radians = 45°

Would you like more details on how the conversions work?

Here are 5 related questions to deepen your understanding:

1. How would you convert 120° into radians?
2. What is the degree equivalent of $\frac{2\pi}{3}$ radians?
3. Can you convert 270° into radians?
4. What is the formula for converting radians back to degrees?
5. How many radians are there in a full circle (360°)?

Tip: Memorize that 180° equals $\pi$ radians for faster conversions between degrees and radians!