Simplify arcsin(1)

Problem

arcsin(1)

Solution

1. Identify the definition of the inverse sine function, where y=arcsin(x) means sin(y)=x for y in the interval [−π/2,π/2]

2. Set up the equation to find the angle y such that sin(y)=1

3. Determine the value within the restricted range [−π/2,π/2] where the sine function equals 1

4. Conclude that since sin(π/2)=1 the value of the expression is π/2

Final Answer

arcsin(1)=π/2

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