RRB Group D · Bite-size lessons
Trigonometry
About 6 min · Mathematics · English
Time worked out from the lesson's 423 words at 150 words a minute, plus a minute for each question.
The official syllabus names this topic only as "Geometry and Trigonometry"; focus on the basics: trigonometric ratios of standard angles, fundamental identities, and simple height-distance problems.
Key ideas
- Trigonometric ratios are defined for acute angles in a right triangle. For angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent, and the reciprocals cot θ = 1/tan θ, sec θ = 1/cos θ, csc θ = 1/sin θ.
- Standard angles (0°, 30°, 45°, 60°, 90°) have exact ratio values that must be memorized.
- Pythagorean identities connect sin, cos, and tan: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ. These are tools for simplification and substitution.
- Complementary angle relations: sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ. Use these when the problem mixes angles like 30° and 60°.
- Height and distance problems translate real-world scenarios (towers, ladders, kites) into right triangles. The "angle of elevation" is measured upward from horizontal; "angle of depression" is measured downward from horizontal.
Watch out for
- Mixing up sin and cos for complementary angles: Students write sin 60° = 1/2 (wrong; sin 60° = √3/2). Always double-check the table.
- Forgetting to simplify surds: Leaving tan 30° as 1/√3 instead of rationalizing to √3/3. While both are correct, answer options may show either form.
- Confusing opposite and adjacent: In tan θ = opposite/adjacent, "opposite" is opposite the angle θ, not opposite the right angle. Draw and label the triangle clearly.
Quick reference
- sin²θ + cos²θ = 1 — the most-used identity; memorize it.
- sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3.
- sin 45° = cos 45° = 1/√2, tan 45° = 1 — the symmetric angle.
- sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3 — complements 30°.
- Angle of elevation/depression = horizontal reference — draw the triangle from the observer's eye level.
Check yourself: 3 questions
1. If sin θ = 3/5, where θ is an acute angle, then find the value of cos θ.
2. A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street?
3. What is the value of (sin 30° + cos 60°) × (sin 60° + cos 30°)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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