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To convert the given angles from degrees to radians, you use the following formula:

\[
\text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180^\circ}\right)
\]

Let's now compute the values for each angle, rounding to 3 decimal places:

### (a) 
- (i) \( 320^\circ \):
  \[
  320^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{320\pi}{180} \approx 5.585 \text{ radians}
  \]

- (ii) \( 20^\circ \):
  \[
  20^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{20\pi}{180} \approx 0.349 \text{ radians}
  \]

### (b)
- (i) \( 270^\circ \):
  \[
  270^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{270\pi}{180} \approx 4.712 \text{ radians}
  \]

- (ii) \( 90^\circ \):
  \[
  90^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{90\pi}{180} \approx 1.571 \text{ radians}
  \]

### (c)
- (i) \( 65^\circ \):
  \[
  65^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{65\pi}{180} \approx 1.134 \text{ radians}
  \]

- (ii) \( 145^\circ \):
  \[
  145^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{145\pi}{180} \approx 2.530 \text{ radians}
  \]

### (d)
- (i) \( 100^\circ \):
  \[
  100^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{100\pi}{180} \approx 1.745 \text{ radians}
  \]

- (ii) \( 83^\circ \):
  \[
  83^\circ \times \left(\frac{\pi}{180^\circ}\right) = \frac{83\pi}{180} \approx 1.449 \text{ radians}
  \]

### Final Answers (rounded to 3 decimal places):
- (a) (i) \( 320^\circ = 5.585 \) radians, (ii) \( 20^\circ = 0.349 \) radians
- (b) (i) \( 270^\circ = 4.712 \) radians, (ii) \( 90^\circ = 1.571 \) radians
- (c) (i) \( 65^\circ = 1.134 \) radians, (ii) \( 145^\circ = 2.530 \) radians
- (d) (i) \( 100^\circ = 1.745 \) radians, (ii) \( 83^\circ = 1.449 \) radians

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you convert radians back to degrees?
2. Why is \( \pi \) used in the conversion between degrees and radians?
3. What is the significance of using radians in trigonometry?
4. How can you quickly estimate small angles in radians?
5. How do you solve trigonometric problems involving both radians and degrees?

**Tip:** Memorize the basic degree-radian conversions for common angles (e.g., \( 180^\circ = \pi \) radians) to speed up calculations.

Express the following angles in radians, correct to 3 decimal places.

Learn how to convert angles from degrees to radians with step-by-step solutions, rounded to 3 decimal places. This exercise covers the formula for converting degrees to radians, suitable for high school trigonometry students.

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