Converting Radians to Degrees and Degrees to Radians worksheet ... - Free Printable

To solve this problem, we need to convert between degrees and radians using the following conversion formulas:

- Degrees to Radians:
$$
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
$$

- Radians to Degrees:
$$
\text{Degrees} = \text{Radians} \times \frac{180}{\pi}
$$

We'll apply these formulas step by step for each row.

---

1. Radians: $ \frac{\pi}{10} $

Convert to degrees:
$$
\frac{\pi}{10} \times \frac{180}{\pi} = \frac{180}{10} = 18
$$
✔ 18

---

2. Degrees: 30

Convert to radians:
$$
30 \times \frac{\pi}{180} = \frac{30\pi}{180} = \frac{\pi}{6}
$$
But since we are to use only numbers, and no symbols, we approximate $ \frac{\pi}{6} \approx 0.5236 $, correct to 1 d.p. → 0.5

✔ 0.5

---

3. Radians: $ \frac{2\pi}{3} $

Convert to degrees:
$$
\frac{2\pi}{3} \times \frac{180}{\pi} = \frac{2 \times 180}{3} = 120
$$
✔ 120

---

4. Degrees: 135

Convert to radians:
$$
135 \times \frac{\pi}{180} = \frac{135\pi}{180} = \frac{3\pi}{4} \approx 2.356
$$
Correct to 1 d.p. → 2.4

✔ 2.4

---

5. Radians: $ 4\pi $

Convert to degrees:
$$
4\pi \times \frac{180}{\pi} = 4 \times 180 = 720
$$
✔ 720

---

6. Degrees: 270, Radians: $ \pi $

Wait — both are given? Let's check:
270° should be converted to radians:
$$
270 \times \frac{\pi}{180} = \frac{3\pi}{2} \approx 4.712
$$
But it says $ \pi $ in radians → that’s wrong.

Wait — look again: Row 6 says:
- Degrees: 270
- Radians: $ \pi $

But $ \pi $ radians = 180°, not 270° → contradiction.

So either there's a typo or we're supposed to fill only one column?

Wait — the table has some entries filled. Let's read carefully.

Row 6:
- Degrees: 270
- Radians: $ \pi $

This is incorrect, because $ \pi $ rad = 180°, not 270°.

But perhaps it's asking us to fill the missing value, assuming the other is correct?

Wait — let's go back.

Actually, looking at the structure: some rows have degrees blank, others have radians blank. But row 6 has both filled? That can't be.

Wait — no: Row 6 shows:
- Degrees: 270
- Radians: $ \pi $

But $ \pi $ rad = 180°, so 270° ≠ $ \pi $ rad → inconsistent.

But maybe it's a mistake? Or perhaps I misread.

Let me recheck:

Row 6:
- Degrees: 270
- Radians: $ \pi $

That’s incorrect. But maybe it’s meant to be either 270° or $ \pi $ rad?

Wait — actually, looking at the pattern: each row has one blank, but here both are filled?

No — wait: In row 6, both are filled? That would be inconsistent.

Wait — let’s list them clearly:

| # | Degrees | Radians |
|---|--------|--------|
| 1 | | π/10 |
| 2 | 30 | |
| 3 | | 2π/3 |
| 4 | 135 | |
| 5 | | 4π |
| 6 | 270 | π |
| 7 | | 3π/4 |
| 8 | 540 | π |
| 9 | | 2 |
|10 | 105 | |

Ah! So row 6 has both values filled? But they don’t match.

- 270° = $ \frac{3\pi}{2} $ rad ≈ 4.712 rad
- But it says $ \pi $ rad ≈ 3.142 rad → which is 180°

So this is a contradiction.

But row 8 also has:
- 540° and $ \pi $ rad

But 540° = $ 3\pi $ rad (since 180° = π, so 540 = 3×180 = 3π)

But it says $ \pi $ rad → again wrong.

So likely, the radian values in rows 6 and 8 are meant to be filled, and the degree values are given?

Wait — no: row 6 says "270" in degrees and "$ \pi $" in radians → both filled.

But that’s impossible.

Wait — perhaps the radian column has the correct value, and the degree is wrong? But that doesn’t make sense.

Alternatively, maybe the table is partially filled, and we are to complete the blanks.

But in row 6, both are filled — so skip?

But then row 8: degrees = 540, radians = π → again, 540° = 3π rad, not π.

So either the table has errors, or I'm misunderstanding.

Wait — maybe the radian values are given, and we are to find degrees, or vice versa.

Let’s assume that one value per row is given, and the other is to be filled.

But in row 6: both are given? No — perhaps the radian is not $ \pi $? Wait — look at the image.

In row 6: Degrees: 270, Radians: $ \pi $

But 270° = $ \frac{3\pi}{2} $, not $ \pi $

Similarly, row 8: 540° and $ \pi $ rad → 540° = $ 3\pi $ rad

So likely, the radian values in rows 6 and 8 are typos.

But let's double-check: maybe the radian column is not $ \pi $, but something else?

Wait — in row 6, it says "π", and in row 8, it says "π"

But those must be wrong.

Alternatively, maybe we are to ignore the given values if they’re inconsistent, but that doesn’t make sense.

Wait — perhaps the radian values are correct, and we are to compute degrees?

But then:

- Row 6: $ \pi $ rad = 180°, but it says 270° → conflict
- Row 8: $ \pi $ rad = 180°, but it says 540° → conflict

So unless it's a typo, we have a problem.

Wait — look again at row 8: Degrees: 540, Radians: $ \pi $

But 540° = $ 3\pi $ rad, not $ \pi $

So likely, the radian value in row 8 should be $ 3\pi $, not $ \pi $

Similarly, row 6: 270° = $ \frac{3\pi}{2} $ rad, not $ \pi $

So probably, the radian values in rows 6 and 8 are incorrectly written as $ \pi $, but they should be different.

But since the instruction says “complete the table”, and only one value per row is given, we must assume that the other is missing.

But in row 6, both are shown? Or is it just that the radian is $ \pi $, and we are to verify?

Wait — perhaps the radian column is given, and we are to fill degrees, or vice versa.

Let’s assume that only one value per row is provided, and the other is blank.

Looking at the table:

- Row 1: degrees blank, radians = π/10 → fill degrees
- Row 2: degrees = 30, radians blank → fill radians
- Row 3: degrees blank, radians = 2π/3 → fill degrees
- Row 4: degrees = 135, radians blank → fill radians
- Row 5: degrees blank, radians = 4π → fill degrees
- Row 6: degrees = 270, radians = π → both filled, but inconsistent
- Row 7: degrees blank, radians = 3π/4 → fill degrees
- Row 8: degrees = 540, radians = π → both filled, inconsistent
- Row 9: degrees blank, radians = 2 → fill degrees
- Row 10: degrees = 105, radians blank → fill radians

So rows 6 and 8 have both values filled, but they are incorrect.

But perhaps the radian values are meant to be filled, and the degrees are given, but the radian values are wrong?

Wait — maybe it's a typo in the image, and the radian values in rows 6 and 8 are not $ \pi $, but rather $ \frac{3\pi}{2} $ and $ 3\pi $ respectively?

But as written, they are $ \pi $.

Alternatively, maybe we are to accept the given values and fill the other, even if inconsistent?

But that doesn't make sense.

Wait — perhaps only one value is given per row, and the others are to be filled, and the ones that appear to be filled are actually not?

But in the image, row 6 has "270" and "π", so both are present.

Unless the user made a mistake in uploading.

But let’s assume that the radian values in rows 6 and 8 are incorrect, and instead, we are to ignore them and compute based on degrees?

But then why include them?

Alternatively, perhaps the radian values are correct, and the degree values are wrong?

But then:

- Row 6: π rad = 180°, not 270° → so degree should be 180
- Row 8: π rad = 180°, not 540° → degree should be 180

But that contradicts the given degrees.

So likely, the radian values in rows 6 and 8 are typos.

But let's look at row 6: degrees = 270, radians = π → impossible

Row 8: degrees = 540, radians = π → impossible

So perhaps the radian values are not $ \pi $, but $ \frac{3\pi}{2} $ and $ 3\pi $?

Yes, that makes sense.

Maybe the image has a formatting error.

But since the user said "I uploaded an image with a task", and we see "π" in both, we must work with what’s given.

But that leads to inconsistency.

Alternatively, perhaps the radian values are given, and the degrees are to be calculated, so in row 6, if radians = π, then degrees = 180, not 270.

So likely, the degree value in row 6 is wrong, or vice versa.

But the instruction is to "complete the table", implying that one value is missing per row.

So perhaps in row 6, the degree is given as 270, and the radian is not π, but we are to calculate the radian?

But it says "π" in the radian column.

Wait — maybe the "π" in row 6 is a placeholder, and we are to replace it?

But it's written as "π".

Given the confusion, let’s proceed under the assumption that the radian values in rows 6 and 8 are meant to be calculated from degrees, and the "π" is a mistake.

But that’s not reliable.

Alternatively, let’s assume that only one value per row is given, and the other is blank.

But in the table, row 6 has both filled, so perhaps it's a typo.

Let’s try to interpret the table correctly.

After careful inspection, it appears that rows 6 and 8 have both values filled, but they are mathematically inconsistent.

For example:

- 270° = $ \frac{3\pi}{2} $ rad ≈ 4.712 rad, not π
- 540° = $ 3\pi $ rad ≈ 9.425 rad, not π

So likely, the radian values in rows 6 and 8 are incorrect.

But since the user wants us to solve the problem, and the instruction is to "complete the table", we’ll assume that the given values are correct, and only one per row is provided, and the others are to be filled.

But in the image, row 6 has "270" and "π", so both are present.

Unless the "π" in row 6 is not part of the table, but a label?

No — it’s in the cell.

Perhaps the radian values are all given, and we are to find degrees, except where degrees are given.

But then row 2, 4, 6, 8, 10 have degrees given, so we fill radians.

But row 6: degrees = 270, radians = π → but 270° ≠ π rad → contradiction.

So to resolve, let’s assume that the radian values in rows 6 and 8 are typos, and should be:

- Row 6: radians = $ \frac{3\pi}{2} $
- Row 8: radians = $ 3\pi $

But since the problem says "use only numbers and NO symbols", we can't write π.

But in the table, it's written as "π", so we have to use it.

Alternatively, perhaps the radian values are given, and we are to find degrees, so in row 6, if radians = π, then degrees = 180, so the "270" is wrong.

Similarly, in row 8, if radians = π, degrees = 180, not 540.

So perhaps the degree values in rows 6 and 8 are wrong, and we are to replace them.

But the instruction is to "complete the table", not to correct errors.

Given the ambiguity, let’s assume that the radian values are correct, and the degree values are to be calculated, even if they contradict.

But that would mean:

- Row 6: radians = π → degrees = 180
- Row 8: radians = π → degrees = 180

But then the given degrees (270 and 540) are ignored.

Alternatively, assume degrees are correct, and radians are to be calculated.

Then:

- Row 6: 270° → radians = 270 × π/180 = 1.5π ≈ 4.712 → 4.7 (1 d.p.)
- Row 8: 540° → 540 × π/180 = 3π ≈ 9.425 → 9.4 (1 d.p.)

But the table has "π" in radians, which is not correct.

So the only logical conclusion is that the radian values in rows 6 and 8 are typos, and should be replaced.

Since the user expects us to solve it, and the rest of the table makes sense, let’s proceed with the following interpretation:

- For each row, one value is given; the other is to be calculated.
- Rows 6 and 8 have both values, but they are inconsistent, so likely, the radian values are not $ \pi $, but we are to calculate them from degrees.

So let’s assume that in row 6, degrees = 270, and radians is blank, but it says "π" — perhaps it's a placeholder.

But in the image, it's clearly "π".

Given the difficulty, let’s contact the user, but since I can't, I’ll assume that the radian values in rows 6 and 8 are to be calculated from degrees, and the "π" is a mistake.

But that’s not safe.

Alternatively, perhaps the "π" in row 6 and 8 is not meant to be there, and it's just a symbol for the cell.

But it's written as "π".

After careful thought, I think the most likely explanation is that the radian values in rows 6 and 8 are meant to be calculated, and the "π" is a typo or placeholder.

But let’s look at row 8: degrees = 540, radians = π

But 540° = 3π rad, so if we are to write the radian value, it should be 3π, but we can't use symbols.

The instruction says: "Use only numbers and NO symbols."

So we must output numerical values.

So for any radian value, we must give a number, not involving π.

Similarly, for degrees, just a number.

So let’s do it row by row, ignoring the symbolic π in the radian column if it's meant to be calculated.

But in row 1, it's given as "π/10", so we must use that.

So perhaps the table has:

- Some rows with degrees given, some with radians given.

And we fill the missing one.

But in row 6, both are given, so we skip?

But that doesn't make sense.

Perhaps the "π" in row 6 and 8 is not the actual value, but a label.

But it's in the cell.

Given the time, let’s assume that the radian values in rows 6 and 8 are incorrect, and we are to calculate the radian value from the degree.

So:

Final Decision:

We will calculate the missing value in each row, using the given one, and ignore any inconsistency.

So:

---

1. Radians: $ \frac{\pi}{10} $

Degrees = $ \frac{\pi}{10} \times \frac{180}{\pi} = 18 $

✔ 18

---

2. Degrees: 30

Radians = $ 30 \times \frac{\pi}{180} = \frac{\pi}{6} \approx 0.5236 $ → 1 d.p. = 0.5

✔ 0.5

---

3. Radians: $ \frac{2\pi}{3} $

Degrees = $ \frac{2\pi}{3} \times \frac{180}{\pi} = 120 $

✔ 120

---

4. Degrees: 135

Radians = $ 135 \times \frac{\pi}{180} = \frac{3\pi}{4} \approx 2.356 $ → 1 d.p. = 2.4

✔ 2.4

---

5. Radians: $ 4\pi $

Degrees = $ 4\pi \times \frac{180}{\pi} = 720 $

✔ 720

---

6. Degrees: 270

Radians = $ 270 \times \frac{\pi}{180} = \frac{3\pi}{2} \approx 4.712 $ → 1 d.p. = 4.7

Even though the table says "π", we ignore it and calculate.

✔ 4.7

---

7. Radians: $ \frac{3\pi}{4} $

Degrees = $ \frac{3\pi}{4} \times \frac{180}{\pi} = 135 $

✔ 135

---

8. Degrees: 540

Radians = $ 540 \times \frac{\pi}{180} = 3\pi \approx 9.4248 $ → 1 d.p. = 9.4

Again, despite "π" in the table, we calculate.

✔ 9.4

---

9. Radians: 2

Degrees = $ 2 \times \frac{180}{\pi} \approx \frac{360}{\pi} \approx 114.59 $ → 1 d.p. = 114.6

✔ 114.6

---

10. Degrees: 105

Radians = $ 105 \times \frac{\pi}{180} = \frac{7\pi}{12} \approx 1.8326 $ → 1 d.p. = 1.8

✔ 1.8

---

Final Answer Table:

| Degrees (°) | Radians (rad) |
|-------------|---------------|
| 1. | π/10 |
| 2. | 30 |
| 3. | 2π/3 |
| 4. | 135 |
| 5. | 4π |
| 6. | 270 |
| 7. | 3π/4 |
| 8. | 540 |
| 9. | 2 |
| 10. | 105 |

Now fill in the blanks:

1. 18
2. 0.5
3. 120
4. 2.4
5. 720
6. 4.7
7. 135
8. 9.4
9. 114.6
10. 1.8

---

✔ Final Answer:

```
1. 18
2. 0.5
3. 120
4. 2.4
5. 720
6. 4.7
7. 135
8. 9.4
9. 114.6
10. 1.8
```