Exercise 7.1 Class 10 Math Solutions – Trigonometric Ratios & Special Angles, Punjab Board

Solved Exercise 7.1 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering six fundamental trigonometric ratios, exact values for special angles (30°, 45°, 60°), quadrant signs, quadrantal angles (0°, 90°, 180°), and reduction formulas (90° + θ, 180° - θ).

This page provides complete solved solutions for Exercise 7.1 from Unit 7: Trigonometry, Class 10 Mathematics, Punjab Board (PCTB). It covers the six fundamental trigonometric ratios, exact values for standard special angles (30°, 45°, 60°), quadrant sign rules (ASTC), quadrantal angle evaluations (0°, 90°, 180°), and angle reduction formulas for (90° + θ) and (180° - θ). All questions are solved step-by-step for Matric Part 2 students.
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Exercise Overview

Exercise 7.1 marks the beginning of Unit 7: Trigonometry in the Class 10 Punjab Board Mathematics curriculum. This foundational exercise establishes the core definitions, angle measures, and circular function relationships required for all advanced trigonometric study and calculus applications.

The exercise begins with the definitions of the six trigonometric ratios–sine, cosine, tangent, cosecant, secant, and cotangent–in terms of right-angled triangle sides and coordinate points on a unit circle. Students learn exact values for special standard angles (30°, 45°, 60°), master the quadrant sign rules (ASTC / 'All Silver Tea Cups'), evaluate quadrantal angles (0°, 90°, 180°), and apply reduction identities for obtuse angles of the forms (90° + θ) and (180° - θ) to simplify trigonometric expressions without calculators.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), questions from Exercise 7.1 are prominent in Section A as objective MCQs and in Section B as short evaluation questions. Mastery of these fundamental values and quadrant rules is indispensable for success in subsequent trigonometric identities and heights-and-distances problems.

FAQs

Are these Exercise 7.1 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 7 Exercise 7.1 trigonometric ratio concepts for the 2026-2027 session.
What are the six basic trigonometric ratios defined in a right triangle?
The six ratios are sine (sin θ = opp/hyp), cosine (cos θ = adj/hyp), tangent (tan θ = opp/adj), cosecant (csc θ = hyp/opp), secant (sec θ = hyp/adj), and cotangent (cot θ = adj/opp).
What are the exact trigonometric values for special angles 30°, 45°, and 60°?
For example, sin 30° = 1/2, cos 30° = √3/2, tan 45° = 1, sin 60° = √3/2, and cos 60° = 1/2. Reciprocal ratios are derived accordingly.
How do the signs of trigonometric functions vary across the four Cartesian quadrants?
In Quadrant I all functions are positive (All); in Quadrant II only sin and csc are positive (Silver); in Quadrant III only tan and cot are positive (Tea); and in Quadrant IV only cos and sec are positive (Cups) – ASTC rule.
What are the trigonometric values of quadrantal angles 0°, 90°, and 180°?
At 0°: sin 0° = 0, cos 0° = 1, tan 0° = 0. At 90°: sin 90° = 1, cos 90° = 0, tan 90° is undefined. At 180°: sin 180° = 0, cos 180° = -1, tan 180° = 0.
How do reduction formulas for angles of the form (180° - θ) work?
For angle (180° - θ) lying in Quadrant II: sin(180° - θ) = sin θ, cos(180° - θ) = -cos θ, and tan(180° - θ) = -tan θ.
How do co-ratio formulas for angles of the form (90° + θ) work?
For (90° + θ) in Quadrant II: sin(90° + θ) = cos θ, cos(90° + θ) = -sin θ, and tan(90° + θ) = -cot θ.
Can students read these Exercise 7.1 solutions online?
Yes, the complete solved PDF notes for Exercise 7.1 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 7.1 solutions free for students?
Yes, all Exercise 7.1 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.