Find the Exact Value sin(1 degree )

Problem

sin(1^∘)

Solution

1. Identify the expression as the sine of one degree.

2. Recognize that 1^∘ is not a standard angle (like 30^∘ 45^∘ or 60^∘ with a simple radical form.

3. Express the value using the conversion from degrees to radians, where 1^∘=π/180 radians.

4. Determine if a simpler algebraic form exists. While sin(1^∘) can be expressed using nested radicals via the half-angle and angle subtraction formulas (e.g., 1^∘=3^∘−2^∘, the resulting expression is extremely complex and typically not considered a standard "exact value" in most contexts.

5. State the exact value in its simplest trigonometric form.

Final Answer

sin(1^∘)=sin(π/180)

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