Trigonometry — practice questions, page 2
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The value of tan5°·tan25°·tan30°·tan65°·tan85° is:The angles of elevation of the top of a vertical tower from two points on the ground, 4 m and 9 m…An aeroplane flying horizontally at a height of 1500√3 m is seen at an elevation of 60° from a…From the top of a 150 m high cliff, the angle of depression of a boat sailing straight towards the…The value of [cos(90° − θ)·secθ·tanθ] ÷ [cosec(90° − θ)·sin(90° − θ)·cot(90° − θ)] is:If A, B and C are the three angles of a triangle, then sin((B + C)/2) equals:If sinθ = 12/13 and θ is acute, the value of cosecθ + cotθ is:The sum of all values of θ in 0° ≤ θ ≤ 90° that satisfy 2sin²θ − 3sinθ + 1 = 0 is:For 0° < θ < 90°, which statement is FALSE?If A + B = 180°, then sinA·cosB + cosA·sinB equals:For how many values of θ with 0° ≤ θ < 360° does 4sinθ + 3cosθ = 6 hold?The minimum value of sec²θ + cosec²θ is:If sinθ − cosθ = 1/2, then sin⁴θ + cos⁴θ equals:If cosecθ − sinθ = a³ and secθ − cosθ = b³, then a²b²(a² + b²) equals:The expression (tanθ + secθ − 1)/(tanθ − secθ + 1) simplifies to:A flagstaff 6 m tall stands upright on the top of a tower. From a point on the ground the angles…The shadow of a vertical tower on level ground is 30 m longer when the sun's altitude is 30° than…A point on a bridge across a river is 4 m above the two banks. From that point the angles of…Two poles of equal height stand on either side of a road 80 m wide. From a point on the road…From the top of a 100 m high tower a car is seen moving straight towards the foot of the tower.…A vertical tower 60 m high stands on level ground with points P and Q on opposite sides of its…If cosθ + secθ = 2, then cos⁵θ + sec⁵θ equals:If tanθ = 1/√7, the value of (cosec²θ − sec²θ)/(cosec²θ + sec²θ) is:If sinθ + cosθ = p and secθ + cosecθ = q, then q(p² − 1) equals:If x = r·sinθ·cosφ, y = r·sinθ·sinφ and z = r·cosθ, then x² + y² + z² equals:
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