Simplify tan(arcsin(x/2))

Problem

tan(arcsin(x/2))

Solution

1. Identify the inner function and set it equal to an angle θ

θ=arcsin(x/2)

2. Rewrite the expression using the definition of the inverse sine function.

sin(θ)=x/2

3. Interpret the sine ratio in terms of a right triangle where sin(θ)=opposite/hypotenuse

opposite=x

hypotenuse=2

4. Apply the Pythagorean theorem to find the adjacent side a

a2+x2=2

a2=4−x2

a=√(,4−x2)

5. Determine the tangent of the angle θ using the ratio tan(θ)=opposite/adjacent

tan(θ)=x/√(,4−x2)

Final Answer

tan(arcsin(x/2))=x/√(,4−x2)

Want more problems? Check here!