Final answer:
The question involves finding coterminal angles for 5π/6 within certain ranges. By subtracting 2π, we find that -7π/6 is a coterminal angle that fits ranges (a) and (d), but not (b) or (c). The strategy used to find these angles involves adding or subtracting 2π.
Step-by-step explanation:
The question is asking us to find coterminal angles for a given angle of 5π/6 within specific ranges. Coterminal angles are angles that share the same initial and terminal sides, but differ by full rotations of 2π radians (360 degrees). To find a coterminal angle within a given range, we add or subtract multiples of 2π until the angle falls within the desired range. Let's approach each range separately:
- (a) Between -π/6 and -2π/3: We subtract 2π from 5π/6 to get a negative angle. As 5π/6 - 2π = -7π/6, which lies within the range -π/6 and -2π/3, -7π/6 is the coterminal angle we seek.
- (b) Between -π/3 and -π/2: Subtracting 2π from 5π/6 gives -7π/6, which is outside the desired range. Therefore, we do not have a coterminal angle in this range.
- (c) Between -π/2 and -π: Again, -7π/6 does not lie within this range, and no other coterminal angle can be found within the desired range.
- (d) Between -π and -3π/2: Since -7π/6 is between -π and -3π/2, it also satisfies this range.
In summary, we can use the strategy of adding or subtracting 2π to find coterminal angles in specific ranges for a given angle.