To convert degrees to radians, we use the formula:

$\text{radians} = \left( \frac{\text{degrees} \times \pi}{180} \right)$

Let's apply this formula to each given angle:

a. $40^\circ$

$\text{radians} = \left( \frac{40 \times \pi}{180} \right) = \left( \frac{40}{180} \right) \pi = \left( \frac{2}{9} \right) \pi$

So, $40^\circ$ is:

$\frac{2}{9} \pi \text{ rad}$

b. $220^\circ$

$\text{radians} = \left( \frac{220 \times \pi}{180} \right) = \left( \frac{220}{180} \right) \pi = \left( \frac{11}{9} \right) \pi$

So, $220^\circ$ is:

$\frac{11}{9} \pi \text{ rad}$

c. $15^\circ$

$\text{radians} = \left( \frac{15 \times \pi}{180} \right) = \left( \frac{15}{180} \right) \pi = \left( \frac{1}{12} \right) \pi$

So, $15^\circ$ is:

$\frac{1}{12} \pi \text{ rad}$

d. $-305^\circ$

$\text{radians} = \left( \frac{-305 \times \pi}{180} \right) = \left( \frac{-305}{180} \right) \pi = \left( \frac{-61}{36} \right) \pi$

So, $-305^\circ$ is:

$\frac{-61}{36} \pi \text{ rad}$

e. $-230^\circ$

$\text{radians} = \left( \frac{-230 \times \pi}{180} \right) = \left( \frac{-230}{180} \right) \pi = \left( \frac{-23}{18} \right) \pi$

So, $-230^\circ$ is:

$\frac{-23}{18} \pi \text{ rad}$

Here are the answers filled in for each question:

a. $\frac{2}{9} \pi \text{ rad}$

b. $\frac{11}{9} \pi \text{ rad}$

c. $\frac{1}{12} \pi \text{ rad}$

d. $\frac{-61}{36} \pi \text{ rad}$

e. $\frac{-23}{18} \pi \text{ rad}$

Would you like any further details or have any questions?

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Relative Questions:

1. How do you convert radians back to degrees?
2. What is the radian measure for $90^\circ$?
3. Can you convert $180^\circ$ to radians?
4. How would you convert $60^\circ$ to radians?
5. What is the formula to convert degrees to radians?
6. What is the radian measure for $270^\circ$?
7. Can you convert $360^\circ$ to radians?
8. What is the simplified fraction form of $225^\circ$ in radians?

Tip: Always simplify the fraction when converting degrees to radians to get the most accurate and easy-to-read answer.