Trigonometry - CBSE 10th Maths

Extra practice questions - Trigomometric ratios, values, identities
1. Concept: Pythagoras Theorem & Trigonometric Ratios

Consider right triangle ABC, right angled at B. If AC = 17 units and BC = 8 units determine all the trigonometric ratios of angle C.

Given sin A = $$frac{12}{37}$, find cos A and tan A. 3. Concept: Trigonometric Ratios & Similar Triangles If C and Z are acute angles and that cos C = cos Z prove that ∠C = ∠Z 4. Concept: Proof: sin A = cos C and cos A = sin C In ΔABC right angled at B, sin C = $\frac{5}{13}$. Find: i. sin A ii. cos A iii. cos C 5. Concept: Pythagoras theorem & Trigonometric Ratios In triangle ABC, right angled at B if sin A = $\frac{1}{2}$, find the value of i. sin C cos A – cos C sin A ii. cos A cos C + sin A sin C 6. Concept: Pythagoras theorem, Quadratic Equations & Trigonometric Ratios In triangle PQR, right angled at Q if PR = 41 units and PQ – QR = 31, find sec2R – tan2R. 7. Concept: Trigonometric Ratios of Specific Values In triangle ABC right angled at B, AB = 12 cm and ∠CAB = 60o. Determine the lengths of the other two sides. 8. Concept: Trigonometric Values of Basic Angles In triangle ABC right angled at B, AB = 5 cm and AC = 10 cm. Determine ∠BAC and ∠BCA. 9. Concept: Trigonometric Values & Linear Equations sin$A + B) = 1 and sin (A – B) = $$frac{1}{2}$; 0o <$A + B) ≤ 90o; ∠A > ∠B.
Find ∠A and ∠B.

10. Concept: Trigonometric Ratio of Specific Values

Find the value of θ in each of the following. θ is an acute angle.
i) 3 sec 2θ = 2 √3
ii) 4 cot 3θ - 4 = 0
iii) 2 sin 2θ = 1

11. Concept: Values of Squares of Trigonometric Ratios

Solve the following: 0o < θ < 90o.