Find the Exact Value sin(1)

Problem

sin(1)

Solution

1. Identify the expression as the sine of 1 radian.

2. Recognize that 1 radian is not one of the standard angles (like 0 π/6 π/4 π/3 or π/2 for which the sine function has a simple algebraic exact value involving square roots.

3. Determine if the value can be expressed in a simpler form. Since 1 is not a rational multiple of π that results in a standard radical expression, the exact value is simply written as sin(1)

4. Note that while sin(1) can be represented as an infinite series or a decimal approximation (≈0.84147, the exact symbolic form is the expression itself.

Final Answer

sin(1)=sin(1)

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