Memorizing special angles in trigonometry can be tough, but there are some easy tricks that helped me a lot. Here are a few that you might find useful too:

1. Get to Know the Unit Circle

The unit circle is super important. It's a circle that helps us understand angles.

Learn these angles in degrees and radians:

• $0^\circ = 0$
• $30^\circ = \frac{\pi}{6}$
• $45^\circ = \frac{\pi}{4}$
• $60^\circ = \frac{\pi}{3}$
• $90^\circ = \frac{\pi}{2}$

Seeing these angles on the circle can make it easier to remember their sine, cosine, and tangent values.

2. Make a Table of Special Angles

Creating a simple table can help you remember the important values:

For $30^\circ$:

• $\sin 30^\circ = \frac{1}{2}$
• $\cos 30^\circ = \frac{\sqrt{3}}{2}$
• $\tan 30^\circ = \frac{1}{\sqrt{3}}$

For $45^\circ$:

• $\sin 45^\circ = \frac{\sqrt{2}}{2}$
• $\cos 45^\circ = \frac{\sqrt{2}}{2}$
• $\tan 45^\circ = 1$

For $60^\circ$:

• $\sin 60^\circ = \frac{\sqrt{3}}{2}$
• $\cos 60^\circ = \frac{1}{2}$
• $\tan 60^\circ = \sqrt{3}$

3. Spotting Patterns and Relationships

Look for patterns in the unit circle. You’ll see that values repeat in different sections, called quadrants. For example, $30^\circ$ and $150^\circ$ have similar sine and cosine values.

4. Use Mnemonic Devices

Make up easy-to-remember phrases. For $30^\circ$, $45^\circ$, and $60^\circ$, you can say: “Half, Root 2, Root 3.” This helps you remember the sine values better.

5. Practice Regularly

Practice is super important! Try quizzing yourself or use flashcards to remember what you learned. The more you see and work with these values, the easier they will get!