Wheel Making 360 Revolutions per Minute — Radians Turned in 1 Second
A wheel makes 360 revolutions in one minute. Find how many radians it turns through in 1 second, converting revolutions per minute into radians per second.
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The Value of 2sin(12°) − sin(72°)
Evaluate 2sin(12°)−sin(72°) by splitting 72° as 60°+12°, then recombining into a single sine of a difference angle using sin18°.
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sinx+sin²x=1: Find (cos¹²x+tan¹²x)+3(cos¹⁰x+tan¹⁰x+cos⁸x+tan⁸x)+(cos⁶x+tan⁶x)
Given sinx+sin²x=1 for x in (0,π/2), evaluate a large trigonometric expression by first proving tanx=cosx, then spotting a binomial cube pattern.
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sec²(tan⁻¹α)+cosec²(cot⁻¹β)=36, α+β=8, α<β — Find α²+β
Given sec²(tan⁻¹α)+cosec²(cot⁻¹β)=36 and α+β=8 with α<β, find α²+β by converting to a system of equations in α+β and αβ.