A. Quadrants and Quadrantal Angles
Completion requirements
A. Quadrants and Quadrantal Angles
In Unit 2, you reviewed quadrants on the Cartesian plane. In Unit 4, you will use the Cartesian plane to define angles terminating in each of the four quadrants.
Notice the positive \(x\)-axis has two corresponding angle measures: \(0^\circ\) and \(360^\circ\). The \(360^\circ\) angle is the result of a full rotation, in the counter-clockwise direction.
Each right angle adds \(90^\circ\), so the angle corresponding to the negative \(x\)-axis will be \({\color{purple}90^\circ + 90^\circ = 180^\circ}\). Adding another right angle will give the angle corresponding to the negative \(y\)-axis, \({\color{orange}180^\circ + 90^\circ = 270^\circ}\). Finally, the addition of one more right angle results in \({\color{green}270^\circ + 90^\circ = 360^\circ}\), which is the angle measure corresponding to one full rotation.
Recall that Quadrant I is located where both the \(x\)-axis and the \(y\)-axis are positive. When examining angles on the Cartesian plane, an angle measure of \(0^\circ\) starts and terminates at the positive \(x\)-axis. From there, positive angles are measured in a counter-clockwise direction. As such, an angle of \(90^\circ\) begins at the positive \(x\)-axis and terminates at the positive \(y\)-axis. Similarly, a \(180^\circ\) angle terminates at the negative \(x\)-axis, and so on.
The angles that terminate on any axis are called quadrantal angles. The angle between the positive \(x\)-axis and the positive \(y\)-axis is a right angle. Therefore, the angle corresponding to the positive \(y\)-axis will be \({\color{blue}0^\circ + 90^\circ = 90^\circ}\).
Notice the positive \(x\)-axis has two corresponding angle measures: \(0^\circ\) and \(360^\circ\). The \(360^\circ\) angle is the result of a full rotation, in the counter-clockwise direction.
Each right angle adds \(90^\circ\), so the angle corresponding to the negative \(x\)-axis will be \({\color{purple}90^\circ + 90^\circ = 180^\circ}\). Adding another right angle will give the angle corresponding to the negative \(y\)-axis, \({\color{orange}180^\circ + 90^\circ = 270^\circ}\). Finally, the addition of one more right angle results in \({\color{green}270^\circ + 90^\circ = 360^\circ}\), which is the angle measure corresponding to one full rotation.