Trigonometry — practice questions, page 9
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QuestionThe number of real angles θ for which sin⁴θ + cos⁴θ = 1/4 is:QuestionThe sum sin²1° + sin²3° + sin²5° + ⋯ + sin²89°, taken over the 45 odd whole degrees from 1° to…QuestionThe value of cos²10° + cos²20° + cos²30° + cos²40° + cos²50° + cos²60° + cos²70° + cos²80° is:QuestionThe value of the product (1 + tan1°)(1 + tan2°)(1 + tan3°) ⋯ (1 + tan44°)(1 + tan45°) is:QuestionThe value of tan6°·tan42°·tan66°·tan78° is:QuestionThe value of tan9° − tan27° − tan63° + tan81° is:QuestionThe value of sin36°·sin72°·sin108°·sin144° is:QuestionIf x = 2cos36°, then x satisfies which equation?QuestionThe three angles of a triangle are in arithmetic progression and the greatest is twice the least.…QuestionIn triangle ABC the angles A, B and C are in arithmetic progression, with B the middle term, and…QuestionFor every angle θ, the sum sin(θ − 60°) + sinθ + sin(θ + 60°) is equal to:QuestionThe smallest positive period of the function f(θ) = sin²θ is:QuestionWhich of these numbers can be the value of sinθ + cosecθ for some real angle θ?QuestionAs θ takes every real value, the expression 3 + 2sin(2θ − 40°) takes exactly the values:QuestionFor every θ at which both sides are defined, sec²θ + cosec²θ is equal to:QuestionIn a right triangle the two legs are in the ratio 1 : 2. If θ is the smaller acute angle, then…QuestionIn a right triangle the hypotenuse measures 41 cm and the shorter leg 9 cm. For the acute angle θ…QuestionIn a right triangle the hypotenuse is exactly twice as long as one of the legs. The smallest angle…QuestionIn triangle ABC, right-angled at B, AB = 8 cm and AC = 17 cm. The value of tanC is:QuestionFor an acute angle θ, tanθ = 2ab/(a² − b²) where a > b > 0. Then sinθ equals:QuestionIn triangle ABC, right-angled at C, the value of sin²A + sin²B + cos²C is:QuestionFrom a point on level ground the angle of elevation of the top of a tower is 45°. On walking 20 m…QuestionTwo towers, 40 m and 60 m high, stand on level ground. A man standing between them, on the line…QuestionA tower has a vertical flagstaff fixed at its top. An observer standing somewhere on level ground…QuestionA vertical pole standing on level ground is looked at twice on the same day: first when the sun's…
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