Find the angle of least positive measure (not equal to the given ...

Question

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5.                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                                                                                  
                                                                          1000°

Accepted Answer

Hello, everyone. We are asked to determine the least positive angle that is co terminal with the given angle 1029 degrees. Our answer choices are a degrees. B 309 degrees C degrees D 411 degrees. So first recall that conterminal angles start in standard position and in the same location, but have a different amount of rotations. Also recall that a full rotation around a circle is degrees. So we are given 1029 degrees. This is a positive angle, but it definitely is not the least positive angle. So to find an angle, co terminal with it, I'm gonna subtract 360 degrees from degrees. And when I do so I get degrees. Now this is still a positive angle. It's still co terminal, but I don't think it's the least one yet because I believe I could take another 360 degrees out of it. So I'm gonna subtract another full rotation of 360 degrees. And when I do so we get 309 degrees. Now, I wanna ask myself, is there another positive angle less than this? That would be co terminal? Well, the only way I'm gonna get another co terminal angle less than it is to subtract degrees. But since this is already less than 360 degrees, if I subtract 360 degrees, I'll get a negative and I don't want a negative. So 309 degrees answer choice B is our answer. Have a nice day.

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Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 1000°