Final answer:
The correct procedure for evaluating arcsin(sin(-57π/10)) is to first find an equivalent angle within the standard range of the arcsin function, which gives us 7π/10 as the exact form answer.
Step-by-step explanation:
The arcsin function, also known as the inverse sine function, returns an angle whose sine is the given number. The range of arcsin is restricted to [-π/2, π/2] or [-90°, 90°], which means it only gives angles in this range. When given an angle outside of this range, you need to find an equivalent angle within this range.
To solve arcsin (sin (-57π/10)), we first need to recognize that -57π/10 is not within the range of the arcsin function. We simplify this by adding multiples of 2π (a full cycle) until the angle lies within the range of [-π/2, π/2]. As -57π/10 is negative, we add 6π (or 60π/10) to get an equivalent angle. This gives us 3π/10.
However, 3π/10 is not within the range of arcsin, so we must find an equivalent angle that is. Since sine function is periodic, sin(θ) = sin(π - θ); to get an angle in the desired range, we use the equivalent angle π - 3π/10, which is 7π/10.
The final answer within the range of arcsin is 7π/10.