Introduction to Trigonometry
27 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 From a point P on level ground, the angle of elevation of the top of a flagpole is 30°. If P is 12 m away from the base of the flagpole, calculate the height of the flagpole (rounded to two decimal places). medium 3 marks Using tangent for height problems
- 2 If sinθ = 3/5 and θ is an acute angle, find cosθ. medium MCQ 2 marks Pythagorean identity for acute angles
- 3 What is the value of sin 30°? easy MCQ 1 mark Basic trigonometric ratio
- 4 If sinθ=5/13 and θ is an acute angle, find tanθ. medium 2 marks Using $\sin^2+\cos^2=1$ to find tangent
- 5 What is the value of cos 60°? easy MCQ 1 mark Trigonometric value of 60°
- 6 If sinα=3/5 and α is acute, find the value of sec(90°-α). hard MCQ 2 marks Complementary angle identity and reciprocal function
- 7 From the top of a building, the angle of depression to a point on the ground 50 m away from the base is 30°. Find the height of the building (in metres, correct to two decimal places). easy 2 marks Angle of depression/elevation
- 8 If sin θ = 12/13 and θ is an acute angle, what is cos θ? medium MCQ 2 marks Pythagorean identity
- 9 Find all acute angles θ (in degrees) satisfying sin θ = cos 2θ. hard 4 marks Trigonometric identities and solving equations
- 10 Find the value of tan 45°. easy 1 mark Basic trigonometric value
- 11 In a right‑angled triangle PQR, ∠ Q = 90°. If ∠ P = 35° and the hypotenuse PR = 15 cm, find the lengths of the other two sides PQ (adjacent to ∠ P) and QR (opposite ∠ P). Give your answers correct to two decimal places. medium 3 marks Using sine and cosine to find unknown sides
- 12 What is the value of tan 30°? easy MCQ 1 mark Standard trigonometric values
- 13 From a point on level ground 40 m away from the base of a lighthouse, the angle of elevation of the top is 22°. Find the height of the lighthouse correct to two decimal places. medium 2 marks Angle of elevation using tangent
- 14 Find the exact value of cos 15°. hard MCQ 2 marks Half‑angle identity for exact values
- 15 What is the value of sin 30°? medium MCQ Trigonometric Values
- 16 What is the value of cos 0°? medium MCQ Trigonometric Values
- 17 Simplify: sin² θ + cos² θ. medium MCQ Trigonometric Identities
- 18 What is tan 45° equal to? medium MCQ Trigonometric Values
- 19 If sin A = 3/5 in a right triangle, what is cos A? medium MCQ Trigonometric Ratios
- 20 What is 1 + tan² θ equal to? medium MCQ Trigonometric Identities
- 21 Find sec 60°. medium MCQ Trigonometric Values
- 22 What is the value of sin 90°? medium MCQ Trigonometric Values
- 23 A ladder 10m long touches a wall at height 5m. Find angle of elevation. medium MCQ Applications of Trigonometry
- 24 Simplify: sin (90° - A). medium MCQ Complementary Angles
- 25 What is the domain, range, or fundamental theorem introduced in 'Introduction to Trigonometry' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 26 What is the derivative or integral formula associated with 'Introduction to Trigonometry'? medium MCQ Calculus & Formulae
- 27 How do you find the solution set or optimum value in 'Introduction to Trigonometry'? medium MCQ Problem Solving & Optimization