Trigonometry — practice questions, page 4
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Which of the following is IMPOSSIBLE for a real angle θ?The shadow of a vertical tower on level ground is 15 m long when the sun's altitude is 60°. When…If cosecθ = √5 and θ is acute, the value of (2 − sin²θ)/(1 + cot²θ) is:If sin⁴θ − cos⁴θ = 1/3, then sin²θ equals:The tops of two vertical poles of heights 20 m and 14 m, standing on level ground, are joined by a…The expression (cos20° − cos40°)/(sin20° + sin40°) equals:If x = a·secθ with a > 0 and θ acute, then √(x² − a²)/x equals:As θ runs over all real values, the expression 4·sinθ·cosθ takes exactly the values:A hill road rises at a steady angle of 30° to the horizontal. A cyclist rides 100 m along this…If sinθ + cosθ = √3·cosθ, then tanθ equals:The value of cos70°/sin20° + cos59°/sin31° − 8sin30° is:In a right triangle the two acute angles are in the ratio 2 : 1. The sine of the larger acute…If x = cosecθ + cotθ, then (x² − 1)/(x² + 1) equals:If tan(A + B) = √3 and tan(A − B) = 1/√3, where 0° < A + B ≤ 90° and A > B, then:The product (1 + cotθ − cosecθ)(1 + tanθ + secθ) simplifies to:If sinθ = 1/3, then the value of sin3θ is:If cosθ = −3/5 and θ lies in the third quadrant, then tanθ equals:If A + B + C = 180°, then tanA + tanB + tanC equals:The only possible value of sinθ satisfying 2sin²θ − 5sinθ + 2 = 0 is:If A + B = 45° and neither angle is 90°, then (1 + tanA)(1 + tanB) equals:A boy whose eyes are 1.5 m above the ground stands 10√3 m from a vertical pole and finds the angle…For every θ with 0° < θ < 90°, the value of sinθ + cosθ satisfies:How many values of θ with 0° ≤ θ < 360° satisfy 2sinθ = tanθ?If sinθ·cosθ = 1/3 and θ is acute, then sinθ + cosθ equals:In a triangle ABC, tanA + tanB = 4 and tanA·tanB = 3. The value of tanC is:
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