Find the Exact Value sin(pi/7)

Problem

sin(π/7)

Solution

1. Identify the angle π/7 as a non-standard angle in trigonometry.

2. Determine if the value can be expressed using basic radicals. The angle π/7 (approximately 25.71 does not have a simple closed-form expression using only square roots, unlike angles such as π/6 or π/4

3. Recognize that the exact value is typically represented as the root of a polynomial. Specifically, sin(π/7) is a root of the equation 64*x6−112*x4+56*x2−7=0

4. Conclude that since there is no simpler radical form, the exact value is written in its trigonometric form.

Final Answer

sin(π/7)=sin(π/7)

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