The 𝑥 is the Positive feelings / Negative feelings axis (

@Feeling

)

The 𝑦 is the High arousal / Low arousal axis (

@Energy

)

There are 32 segments on this wheel corresponding to 32 Emotions (in the

@Spectrum 1 - 1⁄𝑥

which are then grouped by octants (

@Spectrum 2 - ⅛

) and quadrants (

@Spectrum 3 - ¼

))

As a full rotation of a circle is always 360°, we can easily determine the max angle θ for each segment (corresponding to the point where a segment ends and the new one starts).

As we can determine the angle θ, once converted in radians and using the

, we can also determine the cosine and sine of each angle, giving us our needed Cartesian Coordinates (𝑥,𝑦).

Note: Because we’ve entered the trigonometry side of maths, the circle starts at Proud on the wheel and we are turning counterclockwise. So it goes from Proud to Confident, to Satisfied, etc... 😊

All of this is done in the base table you’ll find in

Well, as we’re already in a unit circle, using cosine and sine, we can also create user-friendly readable scales (/10) for our axes 𝑥 and 𝑦 😊.

This allows us, when using the tracker, to retrieve any given segment (circular sector) on the wheel.

This is possible thanks to the fact that trigonometric functions, such as sine and cosine, react in a very specific way in each quadrant of a unit circle 😊, as shown in this chart used to convert degrees to radians and vice-versa (