Many students find this chapter confusing at first — but once you crack the Pandit Badri Prasad Trick, trust me, it becomes one of the easiest scoring topics.
✅ The 3 Sides of a Right-Angle Triangle
Before jumping into ratios, know the 3 sides:
1️⃣ Perpendicular (Opposite Side) — side opposite to the given angle (except the right angle).
2️⃣ Base (Adjacent Side) — side next to the given angle (except the hypotenuse).
3️⃣ Hypotenuse — longest side, always opposite the right angle.
🔑 The Magic Trick: Pandit Badri Prasad
Every Class 10 student must know this:
Pandit Badri Prasad Har Har Bole
It helps you remember all 6 ratios:
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Sin θ = Perpendicular / Hypotenuse
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Cos θ = Base / Hypotenuse
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Tan θ = Perpendicular / Base
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Cosec θ = Hypotenuse / Perpendicular
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Sec θ = Hypotenuse / Base
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Cot θ = Base / Perpendicular
Watch this Video to understand this Magic Trick of Pandit Badri Prasad 👇👇👇👇
List of 6 Trigonometric Ratios
| Ratio | Full Name | Formula | Reciprocal |
|---|---|---|---|
| Sin θ | Sine | P / H | 1 / Cosec θ |
| Cos θ | Cosine | B / H | 1 / Sec θ |
| Tan θ | Tangent | P / B | 1 / Cot θ |
| Cosec θ | Cosecant | H / P | 1 / Sin θ |
| Sec θ | Secant | H / B | 1 / Cos θ |
| Cot θ | Cotangent | B / P | 1 / Tan θ |
📐 Example 1: Easy Triangle
Given:
In triangle ABC, ∠B = 90°, AB = 3 cm, BC = 4 cm.
By Pythagoras,
AC = √(AB² + BC²) = √(9 + 16) = 5 cm.
So,
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P = AB = 3 cm (Opposite to ∠A)
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B = BC = 4 cm (Adjacent to ∠A)
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H = AC = 5 cm
✅ Trigonometric Ratios for ∠A:
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Sin A = P/H = 3/5 = 0.6
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Cos A = B/H = 4/5 = 0.8
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Tan A = P/B = 3/4 = 0.75
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Cosec A = H/P = 5/3 ≈ 1.67
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Sec A = H/B = 5/4 = 1.25
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Cot A = B/P = 4/3 ≈ 1.33
✅ Common Mistakes to Avoid
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Mixing up Base & Perpendicular.
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Not identifying the angle correctly.
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Forgetting that hypotenuse is always the longest side.
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Using degrees & radians wrongly.
🧮 Real-Life Uses
Trigonometry isn’t just textbook stuff!
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Engineers use it to design bridges.
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Astronomers measure distances to stars.
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Surveyors map land.
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Pilots calculate flight paths.
✅ FAQs
Q1: Which side is hypotenuse?
Always opposite the right angle.
Q2: How to remember all ratios?
Use the mnemonic Pandit Badri Prasad Har Har Bole Sona.
Q3: What is the reciprocal of Tan θ?
Cot θ.
Q4: What if I get confused in exam?
Draw triangle, label sides, write mnemonic — problem solved.
Q5: Are degrees & radians same?
No, but in Class 10 we mostly use degrees.
Conclusion
Trigonometry is like a puzzle — once you fix which side is where, solving becomes fun.
Practice is key. Don’t just read — draw triangles, solve real sums, write down Pandit Badri Prasad 10 times.
And remember — you can score full marks in this chapter!
✅ About the Author
Aman Sir, founder of Maths Vidya Institute, has over 14 years of experience teaching CBSE Maths for Classes 9–12. He loves helping students master tough topics with easy tricks and relatable examples.
