If the arcs of the same length in two circles subtend angles of 70° and 120° at their respective centres, determine the ratio of their radii.

Domain and range of sin(x) are ______, respectively.

Let α and β respectively be the maximum and the minimum values of the function f(θ) = 4(sin4(7π2 - θ) + sin4(11π + θ)) - 2(sin6(3π2 - θ) + sin6(9π - θ)), θ ∈ &mathbb{R}. Then α + 2β is equal to:

The range of the function f(x) = 2|sin x + cos x| - √2 is: