Find the Exact Value arctan(24/7)

Problem

arctan(24/7)

Solution

1. Identify the expression as the inverse tangent of a ratio, which represents an angle θ such that tan(θ)=24/7

2. Recognize that 24/7 is not a value associated with the standard angles (like 30 45 or 60 on the unit circle.

3. Determine if the expression can be simplified further. Since 24 and 7 are the legs of a Pythagorean triple (7,24,25) the angle can be described using other inverse trigonometric functions, but the exact value in radians or degrees cannot be written without the arctan() notation or a decimal approximation.

4. Conclude that the exact value is the expression itself, as it represents a specific unique angle in the interval (−π/2,π/2)

Final Answer

arctan(24/7)=arctan(24/7)

Want more problems? Check here!