Trigonometry | Part -5

Memorizing Trigonometric Ratios Using Your Fingers: A Fun and Easy Technique

Recalling the sine, cosine, and tangent values for key angles such as 0°, 30°, 45°, 60°, and 90° can be challenging at times. But what if you could use your own hands as a simple, portable calculator? Yes, your fingers hold the key to mastering these ratios effortlessly! Let’s explore this fascinating and interactive finger technique to memorize trigonometric values.

The Finger Trick Explained

Imagine you have your left hand in front of you with your palm facing up. Assign each finger to a special angle as follows (from left pinky to right thumb):

• Little finger: 0°
• Ring finger: 30°
• Middle finger: 45°
• Index finger: 60°
• Thumb: 90°

To determine the sine or cosine of a given angle, bend the finger that corresponds to that angle and count the fingers on both sides of it.

How to Find Sine Values

To find sin θ for the angle θ corresponding to the folded finger:

1. Count how many fingers are on the left side of the folded one, including the folded finger itself. Let this count be n.
2. Calculate √n / 2.
3. This gives you the sine value for the selected angle.

How to Find Cosine Values

To find cos θ:

1. Count the number of fingers to the right of the folded finger (including the folded finger itself) — call this number m.
2. Calculate √m / 2.
3. The result is the cosine of the angle.

Example: How to Determine sin 45° and cos 45° Using the Finger Method

Let’s say you need to determine the sine and cosine values for 45°, which corresponds to the middle finger in this method. Fold down your middle finger:

• Fingers to the left (little and ring fingers + folded middle finger) = 3 → sin 45° = √3 / 2 ≈ 0.866 (approximate value)
• Fingers to the right (middle finger + index and thumb) = 3 → cos 45° = √3 / 2 ≈ 0.866 (approximate value)

Note: For 45°, since the numbers on both sides are equal, sin and cos are equal, which matches what we know.

Finding Tangent Values

Once you have sine and cosine, calculating tangent is easy:

tan θ = sin θ / cos θ
  

Using the finger method, simply divide the sine value by the cosine value for your desired angle.

Why This Technique Works

This finger mnemonic works because the number of fingers on either side directly correlates to the well-known square root fractions in sine and cosine values for these special angles. It’s a natural, intuitive way to visualize and remember the values without needing to memorize tables.

Practice Makes Perfect

Try using this technique regularly when solving trigonometric problems or during study sessions. Over time, you’ll find it faster and more fun than rote memorization!

• Assign each finger to a special angle (0°, 30°, 45°, 60°, 90°).
• Fold the finger for the angle you want to find.
• Use the count of fingers on each side to calculate sine and cosine.
• Calculate tangent by dividing sine by cosine.
• Practice regularly for quick recall and better understanding.

So next time you struggle to remember those tricky trigonometric ratios, just look at your hand — your fingers will do the math for you!