Trigonometry — practice questions, page 5
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How many values of θ with 0° ≤ θ < 360° satisfy 3sin²θ − sinθ − 2 = 0?If A + B = 60° and tanA + tanB = 3, then tanA·tanB equals:Which statement is correct for every θ with 0° < θ < 45°?From the bottom and from the top of a 15 m tall building, the angles of elevation of the top of a…Expressed in terms of sin3θ, the value of sin³θ is:If A, B and C are the angles of a triangle, then cotA·cotB + cotB·cotC + cotC·cotA equals:The number of values of θ with 0° ≤ θ < 360° for which sin3θ = 0 is:If sinθ < 0 and cotθ > 0, then θ lies in the:A student is told that sinθ·cosθ = 3/5 for some angle θ and concludes that sinθ + cosθ = √(11/5).…Given sin18° = (√5 − 1)/4 and cos36° = (√5 + 1)/4, the value of cos²36° − sin²18° is:If tan(θ/2) = 2, then sinθ + cosθ equals:In the range 0° ≤ θ ≤ 180°, the solution set of 2cos²θ − 5sinθ + 1 = 0 is:If A, B and C are the angles of a triangle, which of these statements is FALSE?For every angle θ, sin(540° − θ) equals:For which of these pairs is (1 + tanA)(1 + tanB) exactly 2?Which of these four numbers is the smallest?From a window 10 m above the ground, the angle of elevation of the top of a lamp post across the…sin18° is a root of which of these quadratic equations?Under the substitution t = tan(θ/2), the equation 3sinθ + 4cosθ = 5 becomes:Which of the following is the correct triple-angle identity for the cosine?If sinθ + cosθ = 7/5 and sinθ > cosθ, then sinθ − cosθ equals:If A, B and C are the angles of a triangle, then sin(B + C − A) equals:How many values of θ with 0° ≤ θ ≤ 360° satisfy cosθ = 1?In triangle ABC, b = 5 cm, c = 8 cm and the angle between them is A = 60°. The length of side a is:If sinA = 3/5 and cosB = 5/13, where A and B are both acute, then sin(A + B) equals:
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