Find the Exact Value arctan(3/5)

Problem

arctan(3/5)

Solution

1. Identify the nature of the expression. The expression arctan(3/5) represents the angle θ in the interval (−π/2,π/2) such that tan(θ)=3/5

2. Check for standard values. The ratio 3/5 (or 0.6 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 3/5 is not a value derived from the square roots of 0, 1, 2, 3u*s(e)*d(i)*n*t*r*i*g*o*n*o*m*e*t*r*i*c*i*d(e)*n*t*i*t*i*e*s(ƒ)*o*r*s(t)*a*n*d(a)*r*d(a)*n*g*l*e*s,t*h*e*e*x*a*c*t*v*a*l*u*e*c*a*n*n*o*t*b*e*e*x*p*r*e*s(s(e))*d(i)*n*t*e*r*m*s(o)*ƒpi$ or simple radicals.

4. Conclude that the expression is already in its simplest exact form.

Final Answer

arctan(3/5)=arctan(3/5)

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