Angles in Standard Position

An angle is in standard position when its vertex sits at the origin of a coordinate system and its initial side lies along the positive $x$-axis.

Once an angle is drawn in standard position, it is classified by where its terminal side ends up:

• Terminal side between the positive $x$-axis and the positive $y$-axis: first-quadrant angle ($0^\circ<\theta<90^\circ$).
• Between the positive $y$-axis and the negative $x$-axis: second-quadrant angle ($90^\circ<\theta<180^\circ$).
• Between the negative $x$-axis and the negative $y$-axis: third-quadrant angle ($180^\circ<\theta<270^\circ$).
• Between the negative $y$-axis and the positive $x$-axis: fourth-quadrant angle ($270^\circ<\theta<360^\circ$). …