Simplify sin(arcsin(( square root of 3)/2))

Problem

sin(arcsin(√(,3)/2))

Solution

1. Identify the composition of functions, which is the sine of the inverse sine of a value x

2. Apply the property of inverse trigonometric functions, which states that sin(arcsin(x))=x for any x in the domain of the inverse sine function, which is [−1,1]

3. Verify that the input value √(,3)/2 is within the interval [−1,1] Since √(,3)≈1.732 then 1.732/2≈0.866 which is within the valid range.

4. Evaluate the expression directly using the identity sin(arcsin(x))=x

Final Answer

sin(arcsin(√(,3)/2))=√(,3)/2

Want more problems? Check here!