Mixing up exact trig values for 30° and 60°

❌ The Mistake in Action

Find the exact value of $\sin 60°$

Wrong: $\sin 60° = \frac{1}{2}$

🧠 Why It Happens

Students confuse which exact value belongs to 30° and which to 60°. The values $\frac{1}{2}$ and $\frac{\sqrt{3}}{2}$ are easy to mix up.

✅ The Fix

Memory aid using the special triangle:

In a 30-60-90 triangle with sides 1, $\sqrt{3}$, 2:

The side opposite the smaller angle (30°) is smaller: 1
The side opposite the larger angle (60°) is larger: $\sqrt{3}$

So:

$\sin 30° = \frac{1}{2}$ (smaller value)
$\sin 60° = \frac{\sqrt{3}}{2}$ (larger value)

Check: $\sin$ increases from 0° to 90°, so $\sin 60° > \sin 30°$. Since $\frac{\sqrt{3}}{2} \approx 0.87 > 0.5 = \frac{1}{2}$, this confirms $\sin 60° = \frac{\sqrt{3}}{2}$.

🔍 Spot the Mistake

Can you identify where this student went wrong?

$\sin 60°$

$= \frac{1}{2}$

Click on the line that contains the error.

📚 Related Topics

Learn more about the underlying maths: