Question

How do you sketch the angle `150^circ` in standard position?

Answer 1

Start at the positive `x`-axis, then rotate left by the desired angle.

Explanation:

Standard position means the first arm of the angle is the positive `x`-axis, and the other arm is placed by rotating counter-clockwise from there, by the amount of the angle.

As a basic example, the symbol `angle` is about a 45° angle in standard position.

To get a feel for where the second arm (called the "terminal arm") will go, remind yourself that the axes themselves meet each other at 90°.

If our angle was 90°, the terminal arm would be on the positive `y`-axis.
If our angle was 180°, it would be on the negative `x`-axis.

Wait! 180° is more than 150°, so our angle is somewhere in quadrant 2. In fact, 150° is 2/3 of the way between 90° and 180°, so our terminal arm will be 2/3 of the way into quadrant 2.

graph{(y+tan(pi/6)x)(y^2-.00001x)=0 [-10, 10, -5, 5]}
(ignore the part of the line in quadrant 4)