Find the Exact Value arcsin(0.76)

Problem

arcsin(0.76)

Solution

1. Identify the task as finding the angle θ such that sin(θ)=0.76 within the restricted range of the inverse sine function, which is [−π/2,π/2]

2. Determine if 0.76 corresponds to a standard unit circle value (like 0,1/2,√(,2)/2,√(,3)/2,1. Since 0.76 is not a standard value, the exact value is expressed using the inverse trigonometric notation itself.

3. Represent the value in its simplest exact form. Without a calculator to provide a decimal approximation, the exact mathematical representation is the expression provided.

Final Answer

arcsin(0.76)=arcsin(0.76)

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