Convert the following degree measures to radians. Write answers as simplified fractions. The pi symbol has already been provided, so do not include it:

a.  40 Question Blank 1 of 5
type your answer...
pi rad.

b.  220 Question Blank 2 of 5
type your answer...
pi rad.
c.  15 Question Blank 3 of 5
type your answer...
pi rad.

d.  -305 Question Blank 4 of 5
type your answer...
pi rad.

e.  -230 Question Blank 5 of 5
type your answer...
pi rad.

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.

Learn how to convert degrees to radians and write answers as simplified fractions using the pi symbol. This problem covers the conversion formula and provides step-by-step solutions for converting various degree measures to radians.

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