Find the Exact Value arcsin(-0.12)

Problem

arcsin(−0.12)

Solution

1. Identify the nature of the value. The value −0.12 is not a standard ratio associated with common angles (like 0 ±1/2 ±√(,2)/2 ±√(,3)/2 or ±1.

2. Determine if an exact algebraic form exists. Since −0.12 is equal to −3/25 the expression arcsin(−3/25) cannot be simplified into a simpler exact form involving π or square roots of integers.

3. Apply the property of odd functions for inverse sine. The function arcsin(x) is odd, meaning arcsin(−x)=−arcsin(x)

4. State the exact value. In mathematics, when a value is not a standard trigonometric ratio, the "exact value" is the expression itself or its equivalent fraction form.

Final Answer

arcsin(−0.12)=arcsin(−3/25)

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