Answer:
a. 110°
Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°
Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°
b. 165°
Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°
Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°
c. -10°
Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°
Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°
Explanation:
When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.
To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.
For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.
For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.
It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.