Trigonometry — practice questions, page 7
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QuestionIn a triangle the side a = 6 cm lies opposite the angle A = 30°. The radius of its circumcircle is:QuestionThe smallest positive angle θ for which cos3θ = −1/2 is:QuestionIn triangle ABC the angles satisfy cosA + cosC = sinB. The triangle must be:QuestionFor every θ, the expression cos⁴θ + sin²θ is identical to:QuestionThe point (x, y) is given by x = a(1 + cosθ) and y = a·sinθ as θ varies. Which equation does it…QuestionFor every angle A, the value of cos²A + cos²(A + 120°) + cos²(A − 120°) is:QuestionIf tanθ + cotθ = 4, then the value of tan⁴θ + cot⁴θ is:QuestionFor an angle θ with tanθ − cotθ = 3, the value of tan²θ + cot²θ is:QuestionIf tanθ + cotθ = k, then sec²θ + cosec²θ written in terms of k is:QuestionIf sinθ + cosθ = 5/4, then sin³θ + cos³θ equals:QuestionAn acute angle θ satisfies sinθ·cosθ = 1/4. The value of sin⁶θ + cos⁶θ is:QuestionIf sinθ − cosθ = 1/√5, then tanθ + cotθ equals:QuestionFor an acute angle θ with 3sinθ = 4cosθ, the value of (4sinθ − 3cosθ)/(2sinθ + 6cosθ) is:QuestionIf tanθ = 5/12 and θ is acute, then (1 + sinθ)(1 − sinθ) ÷ [(1 + cosθ)(1 − cosθ)] equals:QuestionIf 20cotθ = 21 and θ is acute, then (secθ − cosecθ)/(secθ + cosecθ) equals:QuestionThe value of sin(180° + θ)·cos(90° − θ) + cos(180° − θ)·sin(90° + θ) is:QuestionThe product tan(90° + θ)·cot(180° − θ) simplifies to:QuestionFor an acute angle θ, cos(270° − θ) is equal to:QuestionThe sum sinθ + sin(180° − θ) + sin(180° + θ) + sin(360° − θ) equals:QuestionA and B are acute angles with tanA = 1/2 and tanB = 1/3. Then A + B equals:QuestionIf sinA = 8/17 and cosB = 12/13, where A and B are both acute, then cos(A − B) equals:QuestionThe value of (tan50° + tan10°)/(1 − tan50°·tan10°) is:QuestionIf cos2θ = 1/9 and θ is acute, then sinθ equals:QuestionIf tan2θ = 4/3 and 2θ is acute, then tanθ equals:QuestionIf sin2θ = 24/25, then (sinθ + cosθ)² equals:
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