mathBeats: Trigonometry Lesson 3 (The Unit Circle Blueprint)

Can all right triangles in the world

Be gathered into one map?

Radius one, a master plan centered at the global headquarters

Don't worry about lengths anymore

What matters is the direction you face

The unit circle blueprint that simplifies calculation

Briefing begins

Fix the hypotenuse to one (unit circle!)

A strategy that leaves only the angle

One arrow from the central headquarters

Its endpoint is our current position

Size disappears, direction remains

All triangles align on one map

Cosine is horizontal, x, our investment

Sine is vertical, y, our sales

Tangent is the slope from HQ to our position

Sales over investment, the language of efficiency

C is Capital, building the foundation: cosine is x!

S is Sales, rising upward: sine is y!

T is Target, the slope toward efficiency

Tangent is y over x (y over x!)

(Zero degrees), the starting line: Capital is max, cosine is one

Investment is perfect, but Sales is still zero, sine is zero

Slope is zero: just starting the engine

(90 degrees), the peak: Capital disappears, cosine is zero

Sales reaches maximum, sine is one

Target goes infinite: growth beyond numbers

(45 degrees), the balance point

Investment equals sales

Cosine equals sine

Tangent stands proud at one!

C is Capital, building the foundation: cosine is x!

S is Sales, rising upward: sine is y!

T is Target, the slope toward efficiency

Tangent is y over x (y over x!)

Move east: cosine grows stronger

Solid investment (Capital)

Move north: sine rises higher

Exploding sales (Sales!)

Change the direction, change the strategy

Now, where is your arrow pointing?

Don't get lost on the unit circle

The moment you read the coordinates, strategy appears

Next lecture: The Politics of Quadrants

Position determines the atmosphere

Stay tuned