Simplify arcsin(-1/( square root of 2))

Problem

arcsin(−1/√(,2))

Solution

1. Identify the range of the inverse sine function, which is [−π/2,π/2]

2. Rationalize the denominator of the input value to recognize a standard trigonometric ratio.

1/√(,2)=√(,2)/2

3. Apply the property of odd functions for inverse sine, which states arcsin(−x)=−arcsin(x)

arcsin(−√(,2)/2)=−arcsin(√(,2)/2)

4. Determine the angle in the interval [0,π/2] whose sine is √(,2)/2 which is π/4

arcsin(√(,2)/2)=π/4

5. Substitute the value back into the expression.

−π/4

Final Answer

arcsin(−1/√(,2))=−π/4

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