Class 10 Maths Chapter 7 Exercise 7.1 Solutions 2026 – Trigonometry Notes PDF

Unit 7: Trigonometry | Exercise 7.1 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 7.1 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.

Measuring Angles Two Different Ways

Before trigonometric ratios can be studied, angles themselves need a precise, flexible way to be measured and described. Exercise 7.1 introduces angles in standard position and the two units used to measure them — degrees, the familiar system from earlier classes, and radians, a new unit based directly on the geometry of a circle.

Key Concepts Covered in Exercise 7.1

Angles in Standard Position

An angle is in standard position when its vertex sits at the origin and its initial arm lies along the positive x-axis. The angle is measured as the rotation from this initial arm to the terminal arm, positive for counter-clockwise rotation and negative for clockwise.

Degree Measure

A full rotation is divided into 360 equal parts called degrees, written with the symbol °. This is the everyday system most students already know from geometry.

Radian Measure

A radian is defined using the circle itself: one radian is the angle subtended at the center by an arc equal in length to the radius. A full rotation equals 2π radians, which gives the key conversion relationship π radians = 180°.

Converting Between Degrees and Radians

To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. Both conversions come directly from the relationship π radians = 180°.

Step-by-Step Solved Examples

Q. No. 1: Convert 60° to radians.

Multiply by π/180: 60 × (π/180)

= 60π/180 = π/3 radians

Q. No. 2: Convert π/4 radians to degrees.

Multiply by 180/π: (π/4) × (180/π)

= 180/4 = 45°

Q. No. 3: Convert 135° to radians, and state which quadrant the angle lies in.

135 × (π/180) = 135π/180 = 3π/4 radians

Since 90° < 135° < 180°, the angle lies in the second quadrant.

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 7.1 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 converting a common angle between degrees and radians
• Short Questions: Direct degree-to-radian or radian-to-degree conversions, like Q. No. 1 and 2 above
• Long Questions: Converting an angle and identifying its quadrant, like Q. No. 3 above

Where This Matters Beyond This Exercise

Every trigonometric ratio calculated in the exercises ahead depends on correctly identifying an angle’s measure and quadrant first, making this exercise the essential starting point for the whole chapter. Radian measure in particular becomes the standard unit in calculus and physics, where angles describe rotational motion and wave behavior.

Common Mistakes Students Make in Exercise 7.1

• Using the wrong conversion factor — multiplying by 180/π when converting degrees to radians, instead of π/180
• Forgetting to simplify the resulting fraction after converting to radians
• Misidentifying the quadrant for angles close to a boundary, such as exactly 90° or 180°
• Treating π as a variable to solve for, rather than a fixed conversion constant

Why This Exercise Matters for the Board Exam

Degree-radian conversions are quick, formula-based, and one of the most reliably repeated question types at the start of the trigonometry paper section. Getting comfortable with both units here prevents confusion later when trigonometric ratios and graphs are expressed in radians rather than degrees.

Quick Links – Chapter 7: Trigonometry

Links for sections other than Exercise 7.1 will be activated as they are published on this site.

Download Exercise 7.1 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 7.1 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. Why do we need radians if degrees already work?

Radians connect an angle directly to the geometry of a circle (arc length divided by radius), which makes many formulas in higher mathematics, physics, and engineering simpler. Both units measure the same thing, just on different scales.

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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