Final answer:
The equation to solve is π/3. However, this would mean sin(x) is -√3/2, which is not possible since the sine function has a maximum value of 1. Therefore, if we correct the possible error and assume sin-1(x) = π/3, the value of x would be √3/2.
Step-by-step explanation:
To solve for x in the equation cos-1(-1/2) + sin-1(x) = π/3, let's first evaluate the inverse cosine term. The value of cos-1(-1/2) corresponds to an angle whose cosine is -1/2. Since cosine is negative in the second and third quadrants and considering the range of the inverse cosine function, this angle is 2π/3 radians (or 120 degrees).
Now we substitute this into the original equation:
2π/3 + sin-1(x) = π/3
Next, we solve for sin-1(x) by subtracting 2π/3 from both sides:
sin-1(x) = π/3 - 2π/3 = -π/3
The sine of -π/3 is -√3/2, but since the range of the inverse sine function is between -π/2 and π/2 inclusive, and the sine function is negative in the fourth and third quadrants, the corresponding angle for sin-1(-√3/2) is not possible because √3/2 is greater than 1. The student must have made a mistake, as sin-1(x) cannot be -π/3 for the given range.
If we assume that the equation meant to be sin-1(x) = π/3, then the value of x would be √3/2.