Class 10 Maths Chapter 7 Exercise 7.2 Solutions 2026 – Trigonometry Notes PDF

Unit 7: Trigonometry | Exercise 7.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 7.2 solutions for Trigonometry have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Six Ratios, One Right Triangle

Every angle in a right triangle (other than the right angle itself) has a fixed relationship to the triangle’s three sides, no matter how big or small the triangle is drawn. Exercise 7.2 introduces the six trigonometric ratios that capture these relationships, building directly on the angle measurement skills from Exercise 7.1.

Key Concepts Covered in Exercise 7.2

Labeling a Right Triangle

For a chosen angle θ in a right triangle, the side opposite θ is called the opposite, the side next to θ (not the right angle) is the adjacent, and the longest side facing the right angle is always the hypotenuse.

The Three Primary Ratios

sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, and tanθ = opposite/adjacent. These three ratios form the foundation that the other three are built from.

The Three Reciprocal Ratios

cosecθ = 1/sinθ = hypotenuse/opposite, secθ = 1/cosθ = hypotenuse/adjacent, and cotθ = 1/tanθ = adjacent/opposite. Each reciprocal ratio simply flips the corresponding primary ratio upside down.

Values at Standard Angles

This exercise also introduces the exact values of sin, cos, and tan at the standard angles 0°, 30°, 45°, 60°, and 90°, which are used repeatedly throughout the rest of the chapter and should be memorized.

Step-by-Step Solved Examples

Q. No. 1: In a right triangle, the side opposite θ is 3, the adjacent side is 4, and the hypotenuse is 5. Find sinθ, cosθ, and tanθ.

sinθ = opposite/hypotenuse = 3/5

cosθ = adjacent/hypotenuse = 4/5

tanθ = opposite/adjacent = 3/4

Q. No. 2: If sinθ = 3/5, find cosecθ.

cosecθ = 1/sinθ = 1/(3/5) = 5/3

Q. No. 3: Find the value of sin30° + cos60°.

sin30° = 1/2, cos60° = 1/2

sin30° + cos60° = 1/2 + 1/2 = 1

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 7.2 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on stating the reciprocal of a given trigonometric ratio
• Short Questions: Finding all three primary ratios from given triangle sides, like Q. No. 1 above
• Long Questions: Evaluating expressions using standard angle values, like Q. No. 3 above

Where This Matters Beyond This Exercise

The six ratios defined here are used in every remaining exercise of this chapter, from proving trigonometric identities to solving right-triangle word problems. Trigonometric ratios are also fundamental to physics (analyzing forces and waves), engineering, and navigation, wherever angles and distances need to be related precisely.

Common Mistakes Students Make in Exercise 7.2

• Confusing which side is opposite versus adjacent, especially when the triangle is drawn at an angle
• Mixing up a ratio with its reciprocal — for example, writing sinθ = hypotenuse/opposite instead of opposite/hypotenuse
• Forgetting the standard angle values and trying to recalculate them from scratch every time
• Using the wrong ratio for a given pair of known and unknown sides

Why This Exercise Matters for the Board Exam

The six trigonometric ratios and the standard angle values are the single most tested foundation in this chapter, appearing directly or indirectly in nearly every later question. Memorizing the standard values precisely (rather than looking them up) saves significant time across the whole trigonometry section of the paper.

Quick Links – Chapter 7: Trigonometry

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Download Exercise 7.2 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 7.2 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. Do I need to memorize all six ratios and their standard values?

Yes — memorizing sin, cos, and tan at 0°, 30°, 45°, 60°, and 90° (and knowing how to find the reciprocal ratios from them) saves significant time throughout the rest of this chapter and is expected knowledge for board exams.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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