Trigonometry — practice questions, page 10
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QuestionA pole 18 m high stands on level ground. When the sun's altitude falls from 45° to 30°, the length…QuestionFrom a point on level ground 48 m from the foot of a vertical tower, the angle of elevation θ of…QuestionFrom the top of a vertical cliff 40 m high, two buoys floating in line with the foot of the cliff…QuestionTwo towers 30 m and 90 m high stand on level ground. From the foot of the taller tower the angle…QuestionFor 0° < θ < 90°, which statement comparing sin⁴θ + cos⁴θ with sin⁶θ + cos⁶θ is true?QuestionApart from 20° itself, the only angle θ with 0° ≤ θ < 360° for which sinθ = sin20° is:QuestionIf x = a·cosθ + b·sinθ and y = a·sinθ − b·cosθ, then x² + y² is equal to:QuestionIf cosecθ + cotθ = 11 and θ is acute, then cosθ equals:QuestionTwo vertical poles stand on level ground. From a point P on the ground the top of pole A, which is…QuestionFor every θ at which it is defined, (sec θ − tan θ)(sec θ + tan θ) + (cosec θ − cot θ)(cosec θ +…QuestionThe equation 8sinθ + 15cosθ = k has a real solution θ exactly when:QuestionIn triangle ABC the sides satisfy a : b : c = 4 : 5 : 6. The cosine of the SMALLEST angle of the…QuestionThe sum of all the angles θ with 0° < θ < 180° for which tan3θ = 1 is:QuestionIf x = tanθ + cotθ and y = tanθ − cotθ, then x² − y² equals:QuestionA student writes: 'Since sin²θ + cos²θ = 1, taking the square root of both sides gives sinθ + cosθ…QuestionA worker rides a builder's hoist that climbs the outside of a tower. When his eye is 12 m above…QuestionFor 0° < θ < 90°, the least value of tanθ + 4cotθ is:QuestionIn triangle ABC, ∠A = 30°, ∠B = 105° and the side a = 8 cm. The length of side c is:QuestionIf 5(secθ − tanθ) = 3, then 5(secθ + tanθ) equals:QuestionA vertical flag mast stands on the top of a hill 50 m high. From a point on the plain in line with…QuestionIf p = a·secθ + b·tanθ and q = a·tanθ + b·secθ, then p² − q² equals:QuestionHow many angles θ with 0° ≤ θ < 360° satisfy cos 2θ = cos θ?QuestionTwo friends, each with eyes 1.5 m above the ground, stand on level ground on the same side of a…QuestionFor every acute angle θ, the value of cot²θ − cos²θ − cot²θ·cos²θ is:QuestionAs θ takes every real value, the least value of 2^(sin²θ) + 2^(cos²θ) is:
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