Class 10 Maths Chapter 8, Introduction to Trigonometry, defines the six trigonometric ratios of an acute angle in a right triangle, derives the exact values of trigonometric ratios at 0°, 30°, 45°, 60° and 90°, and proves the three fundamental Pythagorean trigonometric identities.
What Class 10 Maths Chapter 8 Covers
8.1 & 8.2 Trigonometric Ratios defines sin A = Opposite/Hypotenuse, cos A = Adjacent/Hypotenuse, tan A = Opposite/Adjacent = sin A / cos A, and their reciprocals csc A, sec A and cot A, showing that these ratios depend only on the angle A and not on the size of the right triangle.
8.3 Trigonometric Ratios of Some Specific Angles uses an isosceles right triangle (45°) and an equilateral triangle (30° and 60°), along with limiting behaviour at 0° and 90°, to build the complete standard table of trigonometric values.
8.4 Trigonometric Identities proves from Pythagoras’s theorem that sin2 A + cos2 A = 1, 1 + tan2 A = sec2 A (0° ≤ A < 90°), and cot2 A + 1 = csc2 A (0° < A ≤ 90°).
Exercises in Chapter 8
- Exercise 8.1 (11 Questions) computes all trigonometric ratios given one ratio or two sides of a right triangle using Pythagoras’s theorem.
- Exercise 8.2 (4 Questions) evaluates expressions using trigonometric values at 0°, 30°, 45°, 60° and 90°, and solves equations like tan (A + B) = √3, tan (A – B) = 1/√3.
- Exercise 8.3 (4 Questions, including the 10-part identity proof question) practices expressing all ratios in terms of sec A and proving classic trigonometric identities.
Read Class 10 Maths Chapter 8 Online
More Chapters
- Previous: Chapter 7: Coordinate Geometry
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FAQ
What are the three fundamental trigonometric identities in Class 10 Maths?
(1) sin2 A + cos2 A = 1; (2) 1 + tan2 A = sec2 A (for 0° ≤ A < 90°); and (3) 1 + cot2 A = csc2 A (for 0° < A ≤ 90°).
What are the values of sin 30°, sin 45°, sin 60° and tan 45°?
sin 30° = ½, sin 45° = 1/√2, sin 60° = √3/2, and tan 45° = 1.