Trigonometric ratios in a right triangle, the ratios of \(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ\), and the identities \(\sin^2 A + \cos^2 A = 1\), \(1 + \tan^2 A = \sec^2 A\), \(1 + \cot^2 A = \csc^2 A\). Our own step-by-step solutions to Exercises 8.1 to 8.3, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. In a right triangle, for acute angle A: \(\sin A = \dfrac{\text{opposite}}{\text{hypotenuse}}\), \(\cos A = \dfrac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan A = \dfrac{\text{opposite}}{\text{adjacent}}\); cosec, sec, cot are their reciprocals. Given one ratio, draw the triangle and find the third side by Pythagoras.
What it tests. Learn the table: \(\sin 30^\circ = \tfrac12\), \(\sin 45^\circ = \tfrac{1}{\sqrt2}\), \(\sin 60^\circ = \tfrac{\sqrt3}{2}\), \(\cos\) in reverse order, \(\tan 30^\circ = \tfrac{1}{\sqrt3}\), \(\tan 45^\circ = 1\), \(\tan 60^\circ = \sqrt3\). Substitute, then simplify surds.
What it tests. Use \(\sin^2 A + \cos^2 A = 1\), \(\sec^2 A - \tan^2 A = 1\), \(\csc^2 A - \cot^2 A = 1\). To prove an identity, start from the more complicated side, write everything in \(\sin\) and \(\cos\) if stuck, and simplify to the other side.
Introduction to Trigonometry has 38 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Introduction to Trigonometry · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.