sin−1(sin(5))

The function sin−1(sin(x)) is the inverse function of sin(x). This means that it "undoes" the operation of the sin(x) function.

Here are the steps to solve sin−1(sin(5)):

1. First, calculate the value of sin(5). The sine of 5 radians is approximately -0.9589242746631385.

2. Then, calculate the inverse sine (sin−1) of this value. The inverse sine of -0.9589242746631385 is approximately -1.2831853071795862 radians.

3. However, the range of the inverse sine function is from -π/2 to π/2, or approximately -1.5707963267948966 to 1.5707963267948966 radians.

4. Therefore, we need to adjust the result to fit within this range. The value -1.2831853071795862 radians is already within this range, so it is the final answer.

So, sin−1(sin(5)) = -1.2831853071795862 radians.