✋ Trick to Remember sin θ and cos θ Values
🎯 Target Angles
We only need to remember these:
0°, 30°, 45°, 60°, 90°
✅ Simple Formula to Remember
sin θ = √(n) / 2
cos θ = √(4 − n) / 2
Where n = 0 to 4 corresponding to angles 0°, 30°, 45°, 60°, 90°
📌 sin θ Table (Using √n / 2)
| θ (Degrees) | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| n Value | 0 | 1 | 2 | 3 | 4 |
| sin θ | √0/2 = 0 | √1/2 = 1/2 | √2/2 | √3/2 | √4/2 = 1 |
📌 cos θ Table (Using √(4−n) / 2)
| θ (Degrees) | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| 4 − n Value | 4 | 3 | 2 | 1 | 0 |
| cos θ | √4/2 = 1 | √3/2 | √2/2 | √1/2 = 1/2 | √0/2 = 0 |
✋ 5-Finger Trick (Visual Trick)
🖐 Place your hand in front of you.
- Number the fingers left to right as: 0°, 30°, 45°, 60°, 90°
- For sin θ, count number of fingers below the bent finger
→ sin θ = √(below fingers) / 2 - For cos θ, count fingers above the bent finger
→ cos θ = √(above fingers) / 2
🎯 Practice with This Table
| Angle | sin θ | cos θ |
|---|---|---|
| 0° | 0 | 1 |
| 30° | 1/2 | √3/2 |
| 45° | √2/2 | √2/2 |
| 60° | √3/2 | 1/2 |
| 90° | 1 | 0 |
🔁 Daily Drill
- Repeat: "0, 1/2, √2/2, √3/2, 1" for sin
- Flip it for cos: "1, √3/2, √2/2, 1/2, 0"
💡 Tip
You don’t need to memorize anything. Just remember 0 to 4 and apply: