Question

Which quadrant \[180 < \theta < 270\] degree lies?

Answer 1

Hint: Degree measurement is based on a circle, which is \[{360^0}\]. If a ray is allowed to rotate one complete revolution counter clockwise around the \[xy\] plane, starting and ending at the positive \[x - axis\], we say that the ray has rotated \[{360^0}\], Its angle measurement would be written \[{360^0}\]

                     

Complete Step-by-step solution
Here the given angle is\[{180^0} < \theta < {270^0}\].
We have the following angle represents in Quadrants:
Quadrant I \[ = {0^0} < \theta < {90^0}\]
Quadrant II \[ = {90^0} < \theta < {180^0}\]
Quadrant III \[ = {180^0} < \theta < {270^0}\]
Quadrant IV \[ = {270^0} < \theta < {360^0}\]
i.e. this lies in Quadrant III as the range of quadrant III is \[ = {270^0} < \theta < {360^0}\]
Initial line: negative \[x - axis\]
Terminal line: negative \[y - axis\]

Note: Now let us know look into the concept to make the concept of quadrants simple., i.e. for Quadrant I: -initial side: positive \[x - axis\]
Terminal side: Positive \[y - axis\]
Counter-clockwise rotation
We swept angle between \[{0^0}\]to\[{90^0}\]