It looks like you've uploaded an image containing a table of angle conversions between
degrees and
radians, but there's no specific problem or question stated in the image. The table shows various angles in degrees converted to radians (and vice versa), using the standard conversion formula:
$$
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
$$
$$
\text{Degrees} = \text{Radians} \times \frac{180}{\pi}
$$
Let me walk through how these conversions work, and then I can help you solve any particular problem if you have one.
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🔁 Conversion Rules:
- To convert
degrees → radians: Multiply by $ \frac{\pi}{180} $
- To convert
radians → degrees: Multiply by $ \frac{180}{\pi} $
---
✔ Examples from the Table:
Let’s verify a few entries:
1.
$ 30^\circ = \frac{\pi}{6} $
$$
30 \times \frac{\pi}{180} = \frac{\pi}{6} \quad \text{✓}
$$
2.
$ -45^\circ = -\frac{\pi}{4} $
$$
-45 \times \frac{\pi}{180} = -\frac{\pi}{4} \quad \text{✓}
$$
3.
$ 180^\circ = \pi $
$$
180 \times \frac{\pi}{180} = \pi \quad \text{✓}
$$
4.
$ 270^\circ = \frac{3\pi}{2} $
$$
270 \times \frac{\pi}{180} = \frac{3\pi}{2} \quad \text{✓}
$$
5.
$ -120^\circ = -\frac{2\pi}{3} $
$$
-120 \times \frac{\pi}{180} = -\frac{2\pi}{3} \quad \text{✓}
$$
6.
$ 360^\circ = 2\pi $
$$
360 \times \frac{\pi}{180} = 2\pi \quad \text{✓}
$$
7.
$ 240^\circ = \frac{4\pi}{3} $
$$
240 \times \frac{\pi}{180} = \frac{4\pi}{3} \quad \text{✓}
$$
All entries in the table are correct.
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📌 Notes:
- Negative angles represent clockwise rotation.
- Angles greater than $ 360^\circ $ or less than $ -360^\circ $ can be reduced modulo $ 360^\circ $ for reference.
- Radians are often expressed in terms of $ \pi $ for exactness.
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If you have a
specific question related to this table — such as:
- Converting a given degree to radians,
- Finding a missing value,
- Understanding why a certain conversion is correct,
- Or solving a trigonometric problem involving these angles,
Please let me know! I'm happy to help with that.
Parent Tip: Review the logic above to help your child master the concept of degrees to radians worksheet.
