Find the Exact Value arctan(3/7)

Problem

arctan(3/7)

Solution

1. Identify the nature of the expression. The expression arctan(3/7) represents the angle θ such that tan(θ)=3/7 within the interval (−π/2,π/2)

2. Check for standard values. The ratio 3/7 does not correspond to any of the standard angles (such as 0,30,45,60,90 typically found on the unit circle.

3. Determine if further simplification is possible. Since 3/7 is not a value derived from standard trigonometric identities or special triangles, the exact value is most accurately expressed in its inverse trigonometric form.

Final Answer

arctan(3/7)=arctan(3/7)

Want more problems? Check here!