Trigonometry — practice questions with answers
89 questions with worked solutions. Open any question to see the full step-by-step answer.
Browse practice questions
If 5 \θ = 4 , find the value of 5 \θ - 3 \θ/5 \θ + 2 \θ .Using standard trigonometric values, evaluate ^2 30^° + ^2 30^° + ^2 45^° .If 3 sin θ + 5 cos θ = 5 and θ is acute (0° < θ < 90°), find 5 sin θ − 3 cos θ.Two ships are on opposite sides of a 100 m high lighthouse. From its top, their angles of…From the top of a 200 m high cliff, the angles of depression of two boats on the same side of the…A tree breaks in a storm. The broken part bends over so that its top touches the ground 8 m from…A flagstaff stands on top of a 20 m high building. From a point on the ground, the angles of…A 1.5 m tall boy stands some distance from a 30 m tall building. As he walks towards the building,…From the top of a 60 m high building, the angles of depression of the top and the bottom of a…An aeroplane flies horizontally at a height of 1500√3 m. From a point on the ground, its angle of…A man on top of a tower watches a car moving straight towards the tower. The angle of depression…From a point 60 m above a still lake, the angle of elevation of a cloud is 30° and the angle of…A 1.6 m tall statue stands on a pedestal. From a point on the ground, the angle of elevation of…A ladder placed in a street at 60° to the ground just reaches a window 6√3 m high on one side.…A sailor on the deck of a ship, 10 m above the water, sees the top of a hill at an elevation of…An aeroplane at a height of 3000 m passes vertically above another aeroplane. At that instant, the…Work out the sum sin²5° + sin²10° + sin²15° + … + sin²90°.If cos(A + B) = 1/2 and sin(A − B) = 1/2, where 0° < A + B ≤ 90° and A > B, find A.Find sec 70° · sin 20° − cos 20° · cosec 70°.Taking odd degrees only, find sin²1° + sin²3° + sin²5° + … + sin²89°.For any angle θ between 0° and 45°, cos²(45° + θ) + cos²(45° − θ) equals4 sin θ = 3 cos θ. Find (sin θ + cos θ)/(sin θ − cos θ).For acute θ with sin θ = 8/17, evaluate (sec θ + tan θ)(1 − sin θ).In triangle ABC, right-angled at C, AC = 20 cm and AB = 29 cm. Find tan A + tan B.If sin θ = (m² − n²)/(m² + n²), with m > n > 0 and θ acute, then tan θ equals
Page 1 of 4 · Next →
Practise Trigonometry free →
10 free questions a day without an account — unlimited with a free account.