Find the Exact Value arctan(2/7)

Problem

arctan(2/7)

Solution

1. Identify the nature of the expression. The expression arctan(2/7) represents the angle θ such that tan(θ)=2/7 within the interval (−π/2,π/2)

2. Check for standard values. The ratio 2/7 does not correspond to any of the standard angles (such as 0 π/6 π/4 π/3 or π/2 typically found on the unit circle.

3. Determine the exact form. Since 2/7 is not a value that results in a simplified multiple of π the exact value is expressed simply as the inverse trigonometric function itself.

Final Answer

arctan(2/7)=arctan(2/7)

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