In this module, we are going to

• look over definitions,
• introduce new notation, and
• work with circles and trigonometric functions.

An angle has three parts: an initial arm and a terminal arm, both of which are rays, and a vertex which is the initial point for both rays.

A standard position angle is positive when the initial arm of the angle is rotated in a counterclockwise direction about the origin to the terminal arm.

A standard position angle is negative when the initial arm of the angle is rotated in a clockwise direction about the origin to the terminal arm.

Sketch the following angles in standard position

a. \(120^{\circ}\)

b. \(-50^{\circ} \)

c. \(\dfrac{\pi}{6}\) rad

d. \(\dfrac{5 \pi}{4}\) rad

Solution

a.

b.

c.

d.

Notice that the axes which form the boundary for the quadrant containing the terminal arm are marked with angle measures. These are provided for reference purposes only.