Trigonometry — practice questions, page 8
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QuestionThe value of 4cot²45° − sec²60° + sin²30° + cos²90° is:QuestionThe value of (sin30° + tan45° − cosec60°)/(sec30° + cos60° + cot45°) is:QuestionFrom a point 20 m above the surface of a lake, the angle of elevation of a cloud is 30° and the…QuestionA tower is 50 m high, and from a point on level ground the angle of elevation of its top is 75°.…QuestionA balloon hovers directly above a point O on a straight level road. Two cars stand on the road on…QuestionA ladder leaning against a vertical wall reaches a window 12 m above the ground and makes an angle…QuestionThe expression √3·sinθ + cosθ is rewritten in the form R·sin(θ + α) with R > 0 and α acute. Then:QuestionAs θ takes all real values, how many integers lie in the range of 9sinθ + 40cosθ?QuestionFor every θ at which it is defined, (cosecθ − cotθ)² is equal to:QuestionFor sinθ ≠ ±cosθ, the expression (sin⁶θ − cos⁶θ)/(sin²θ − cos²θ) simplifies to:QuestionIf sinθ and cosθ are the two roots of the quadratic equation ax² + bx + c = 0, then a, b and c…QuestionIn triangle PQR, right-angled at Q, PQ = 5 cm and QR = 12 cm. The value of sinP + cosR is:QuestionThe 180 numbers cos1°, cos2°, cos3°, …, cos180° are all added together. The total is:QuestionFor every real θ, the value of 3cos²θ + 4sin²θ lies between:QuestionThe angles A + B and A − B are both acute and tan(A + B)·tan(A − B) = 1. Then A equals:QuestionIf x·sin45°·cos45° = tan45°·cosec30°, then x equals:QuestionA point P lies 10 units from the origin O, and OP makes an angle of 30° with the positive x-axis.…QuestionIf tanθ + secθ = k, where k > 0, then cosθ written in terms of k is:QuestionIf (1 + sinθ)/(1 − sinθ) = 9 and θ is acute, then secθ + tanθ equals:QuestionFor an acute angle θ, the expression (1 + sinθ)/(1 − sinθ) − (1 − sinθ)/(1 + sinθ) simplifies to:QuestionIf cosθ/(1 − sinθ) + cosθ/(1 + sinθ) = 4 and θ is acute, then θ equals:QuestionIf sin⁴θ + cos⁴θ = 7/9, then sin⁸θ + cos⁸θ equals:QuestionFor every angle θ, the value of 3(sin⁴θ + cos⁴θ) − 2(sin⁶θ + cos⁶θ) is:QuestionIf sin⁴θ/a + cos⁴θ/b = 1/(a + b), where a and b are positive, then sin⁸θ/a³ + cos⁸θ/b³ equals:QuestionFor 0° < θ < 90°, the expression sin⁸θ + cos⁸θ takes its smallest value when θ equals:
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