Trigonometric Ratios
SSC GD Exam Preparation - Quantitative Aptitude
Trigonometry is a key topic in competitive exams, mainly for angles, heights, distances, and triangle problems. Understanding trigonometric ratios is essential.
🔹 1. Basic Trigonometric Ratios in a Right-Angled Triangle
Triangle Terminology:
Hypotenuse
Longest side (opposite right angle)
Opposite
Side opposite the angle θ
Adjacent
Side next to angle θ
| Ratio | Formula | Example |
|---|---|---|
| Sine (sin) | sin θ = Opposite / Hypotenuse | sin A = a / c |
| Cosine (cos) | cos θ = Adjacent / Hypotenuse | cos A = b / c |
| Tangent (tan) | tan θ = Opposite / Adjacent | tan A = a / b |
| Cosecant (csc) | csc θ = 1 / sin θ = Hypotenuse / Opposite | csc A = c / a |
| Secant (sec) | sec θ = 1 / cos θ = Hypotenuse / Adjacent | sec A = c / b |
| Cotangent (cot) | cot θ = 1 / tan θ = Adjacent / Opposite | cot A = b / a |
🔹 2. Important Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ
🔹 3. Common Angle Values
| Angle θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. In a right triangle, opposite = 3, hypotenuse = 5. Find sin θ.
View Answer
sin θ = 3 / 5
Q2. Adjacent = 4, hypotenuse = 5. Find cos θ.
View Answer
cos θ = 4 / 5
Q3. Opposite = 3, adjacent = 4. Find tan θ.
View Answer
tan θ = 3 / 4
Q4. sin θ = 1/2. Find θ.
View Answer
θ = 30°
Q5. cos θ = √2 / 2. Find θ.
View Answer
θ = 45°
Q6. tan θ = √3. Find θ.
View Answer
θ = 60°
Q7. Hypotenuse = 10, opposite = 6. Find csc θ.
View Answer
csc θ = 10 / 6 = 5/3
Q8. Hypotenuse = 13, adjacent = 5. Find sec θ.
View Answer
sec θ = 13 / 5
Q9. Opposite = 7, adjacent = 24. Find cot θ.
View Answer
cot θ = 24 / 7
Q10. Verify sin²θ + cos²θ for sin θ = 3/5, cos θ = 4/5.
View Answer
(3/5)² + (4/5)² = 9/25 + 16/25 = 25/25 = 1 ✅
Q11. Find tan θ if sin θ = 4/5, cos θ = 3/5.
View Answer
tan θ = sin θ / cos θ = (4/5)/(3/5) = 4/3
Q12. Find cot θ if tan θ = 2.
View Answer
cot θ = 1 / 2
Q13. sin θ = 0.6, find cos θ.
View Answer
cos θ = √(1 – 0.6²) = √(1 – 0.36) = √0.64 = 0.8
Q14. For θ = 30°, find all six trigonometric ratios.
View Answer
sin = 1/2, cos = √3/2, tan = 1/√3, csc = 2, sec = 2/√3, cot = √3
Q15. If cot θ = 3/4, find tan θ.
View Answer
tan θ = 1 / cot θ = 4 / 3
✅ SSC GD Exam Strategy
🟢 Memorize all six trigonometric ratios and their formulas
🟢 Practice common angle values (0°, 30°, 45°, 60°, 90°)
🟢 Master trigonometric identities for quick calculations
🟢 Learn to identify opposite, adjacent, and hypotenuse quickly
🟢 Time yourself - aim for 20-35 seconds per trigonometry problem
You've completed Trigonometry: Basic Ratios!
SSC GD Tip: Mastering basic trigonometric ratios is fundamental for solving height and distance problems efficiently. Remember the SOH-CAH-TOA mnemonic: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. Regular practice with previous year SSC GD questions will help you recognize which ratio to apply in different scenarios. Pay special attention to common angle values and trigonometric identities as they frequently appear in exams. Understanding these basics will build a strong foundation for more advanced trigonometry concepts.
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