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.

  2. Concept: Trigonometric Ratios

    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.
    i) 2 sin2 θ = \\frac{3}{2})
    ii) 3 tan2 θ + 2 = 3
    iii) cos2 θ - \\frac{1}{4}) = \\frac{1}{2})

  12. Concept: Trigonometric Value of Basic Angles

    Evaluate the following:
    i) cosec2 45o + tan2 45o – 3sin2 90o
    ii) cos 60o cos 30o – sin 60o sin 30o
    iii) \\frac{\text{tan ⁡60 − tan 30}}{\text{1 + tan⁡ 60 tan 30}})

  13. Concept: Trigonometric Ratio of Specific Values

    Find the value of x in each of the following:
    i) cosec 3x = \\frac{\text{cot ⁡30 + cot 60}}{\text{1 + cot⁡ 30 cot 60}})
    ii) cos x = 2 sin 45o cos 45o – sin 30o

  14. Concept: Trigonometric Ratio & Fractions

    If θ is an acute angle and \\frac{\text{sin θ + 1}}{\text{sin θ - 1}}) = \\frac{√3 + 2}{√3 − 2}) , find θ.

  15. Concept: Trigonometric Ratio & Linear Equation in 3 variables

    In an acute angle triangle ABC, sin(A + B + C) = \\frac{1}{2}), cot(A – B + C) = 0 and cos(B + C– A) = \\frac{1}{2}). What are the values of A, B, and C?