Final answer:
Gabby's first error in solving the trigonometric inequality could be associated with incorrect simplification or an inappropriate graphical method which is less accurate than an analytical approach. Simplifying the inequality using proper trigonometric identities and solving it analytically would avoid such errors.
Step-by-step explanation:
The student Gabriel made an error in solving the trigonometric inequality. To locate the error, let's review the steps that should be taken to address this problem correctly. The first step is to ensure that we correctly simplify the inequality, ensuring all trigonometric identities are applied correctly. After simplification, it is important to solve for x over the given interval, 0≤x≤2π radians, analytically.
Using the graphical method by setting y equal to both sides and graphing may introduce inaccuracies. Rather than relying on the intersections of the graphs, an analytical solution will yield a precise set of x values that satisfy the inequality. If Gabrielle did not apply the correct trigonometric identities during simplification or did not handle the division by sin(x) correctly, those could be potential sources of error. Without the exact steps Gabby performed, we cannot determine where the first error was made. It is essential to transform all functions to sine and cosine, perform algebraic manipulations, and then solve the inequality possibly by finding critical points and testing intervals on the unit circle.