Reference Angle

The notion reference angle would be the very FIRST thing to understand before solving any trig equations.

First thing first, it’s always the angel with X-axis and Terminal Ray.

What is it for:
In trigonometry, if angles have the same reference angle, then they do have the SAME trig function values.
e.g. sin(x) = sin(π-x),
cos(x) = cos(2π-x).

Math bits notebook.
Math open reference.

Features of a reference angle:

• It’s always LESS THAN 90°.
• It’s always POSITIVE.
• It’s always the angle between the Side and the X-axis.

How to get the reference angle θ:

• Quadrant I: θ
• Quadrant II: π - θ
• Quadrant III: θ - π
• Quadrant IV: 2π - θ

Angles in Standard Position

Regard to the reference angle, the angles in standard positionmeans the ORIGINAL angle.

e.g. There’s an angle θ = 330°. So 330° is the angle in standard position, and 30° is its reference angle.

Tricks:

To imagine a Diving Athlete finished a ROLLING before hits water, she rolled may be 2 rounds, aka. 720°, and she made a 45° angle with her body and the surface of water.

Reference Triangles

A reference triangle is formed by "dropping" a PERPENDICULAR line from the terminal ray of a standard position angle to the X-axis. Remember, it must be drawn to the x-axis.

Math is fun.