Simplify sin(arctan( square root of 3))

Problem

sin(arctan(√(,3)))

Solution

1. Evaluate the inner expression arctan(√(,3)) by finding the angle θ in the interval (−π/2,π/2) such that tan(θ)=√(,3)

2. Identify the angle θ=π/3 (or 60 because tan(π/3)=√(,3)

3. Substitute the value of the angle back into the outer function to get sin(π/3)

4. Calculate the sine of the angle using the unit circle or special triangles.

5. Determine that sin(π/3)=√(,3)/2

Final Answer

sin(arctan(√(,3)))=√(,3)/2

Want more problems? Check here!