Trigonometry — practice questions with answers
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If sinθ = 3/5 and θ is acute, then tanθ equals:If sinA + cosA = √2, then sinA·cosA equals:From the top of a lighthouse 75 m high, the angle of depression of a ship is 45°. The distance of…The value of the product tan1°·tan2°·tan3° ⋯ tan89° is:If 3cotθ = 4, then the value of (5sinθ − 3cosθ) / (5sinθ + 3cosθ) is:The expression (sinθ + cosecθ)² + (cosθ + secθ)² simplifies to:If secθ + tanθ = 5, then secθ − tanθ equals:The expression (1 + tan²A) / (1 + cot²A) simplifies to:The value of 4(sin⁴60° + cos⁴30°) − 3(tan²60° − tan²45°) is:If sin(A + B) = 1 and sin(A − B) = 1/2, where 0° ≤ A + B ≤ 90° and A > B, then:If tanθ + cotθ = 2, then tan³θ + cot³θ equals:A tower is 30 m high. As an observer walks straight towards its foot, the angle of elevation of…From the top of a building 60 m high, the angles of depression of the top and the bottom of a lamp…If cosecθ − cotθ = 1/3, then cosecθ + cotθ equals:The expression tanA/(1 − cotA) + cotA/(1 − tanA) simplifies to:The expression sinθ/(1 + cosθ) + (1 + cosθ)/sinθ simplifies to:If A + B = 90°, then (tanA·tanB + tanA·cotB)/(sinA·secB) − sin²B/cos²A simplifies to:The angle of elevation of the top of a hill from the foot of a 20 m tower is 60°, and the angle of…If 7sin²θ + 3cos²θ = 4 and θ is acute, then tanθ equals:If a·cosθ − b·sinθ = c, then a·sinθ + b·cosθ equals:If tanθ = 3/4 and θ is acute, the value of (sinθ + cosθ)/(sinθ − cosθ) is:If sin⁴θ + cos⁴θ = 5/8 and θ is acute, then sinθ·cosθ equals:If x = tanθ + sinθ and y = tanθ − sinθ, which relation holds?How many values of θ with 0° < θ < 360° satisfy 2cos²θ + cosθ − 1 = 0?The value of sin²1° + sin²2° + sin²3° + ⋯ + sin²89° is:
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