The radian measure of an angle in standard position is -2023π/6. In what quadrant will its terminal side lies?

To determine the quadrant in which the terminal side of the angle lies, we first need to convert the radian measure to a value between 0 and 2π (or 0 and 360 degrees if you prefer degrees).

1. The radian measure of the angle is -2023π/6. We can simplify this by dividing both the numerator and the denominator by π to get -2023/6.

2. Next, we divide -2023 by 6 to get approximately -337.17.

3. Since this value is negative, it means the angle is measured in the clockwise direction.

4. To find the equivalent positive angle, we can add 360 until we get a positive value. When we add 360 to -337.17, we get 22.83.

5. Now, we need to determine in which quadrant this angle lies. An angle of 22.83 degrees lies in the first quadrant.

So, the terminal side of the angle -2023π/6 lies in the first quadrant.