How to change the radian number to 2K π + α (0 ≤ α < 2 π) form? Read a lot of Baidu know, or do not understand For example: - 46 π / 3 Don't give me the solution directly, I want the explanation About the value of wealth... I will give more after reading the answer

How to change the radian number to 2K π + α (0 ≤ α < 2 π) form? Read a lot of Baidu know, or do not understand For example: - 46 π / 3 Don't give me the solution directly, I want the explanation About the value of wealth... I will give more after reading the answer

In fact, it's very simple to know that "the arc length equals to the radius of the circle, and the central angle of the arc is 1 radian". Then the circumference is 2 π R, and the corresponding radian is 2 π. SO 2 π rad is equivalent to 360 degrees, so we have the so-called formula 2 π /. 360 degrees = radians / angular degrees, which is about a fraction. Similarly, 2K π (2 π * k) is equivalent to 360 degrees * K,

-How do 108 ° and - 225 ° turn into 2K π + a (0 ≤ a < 2 π,

-108°
=2kπ+2π-108°
=2kπ+360°-108°
=2kπ+252°
-108°
=2kπ+2π-225°
=2kπ+360°-225°
=2kπ+135°

How K π and 2K π

It means taking Union
{x | 2K π ≤ x ≤ 2K π + π / 6 or x = 2K π + π, K belongs to Z}
If it's an intersection
empty set