Trigonometry & the Unit Circle

Description

This animation shows the unit circle definition of sine and cosine. A point traces the circle as angle θ sweeps from 0 to 2π. Vertical (sin) and horizontal (cos) projections are drawn in real time. Simultaneously, sin and cos waves trace out on a graph panel to the right, creating an intuitive visual connection between circular motion and wave graphs.

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Phases

#	Phase Name	Duration	Description
1	Setup	5s	Draw axes, unit circle, formula labels
2	Key angle labels	4s	Mark 0, π/6, π/4, π/3, π/2, π on circle
3	Point tracing	25s	θ animates 0 → 2π; sin (red) and cos (blue) projections drawn live; wave graphs trace right panel
4	Summary	6s	All elements visible; sin²θ + cos²θ = 1 identity shown

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Layout

+------------------------+------------------------+
|                        |  sin/cos waves (right) |
|   Unit Circle (left)   |                        |
|       O────────•(θ)    |  ~~~sin wave (red)~~~  |
|       |sin|    |       |                        |
|       +---cos--+       |  ~~~cos wave (blue)~~~ |
|                        |                        |
| θ = 1.57   [angle val] |                        |
+------------------------+------------------------+

Area Descriptions

Area	Content	Notes
Left half	Unit circle + axes + point + projections	Main geometric view
Right half	Axes for wave graphs	sin in RED, cos in BLUE traced as θ increases
Bottom left	θ value readout	Driven by ValueTracker
Circle	Key angle dots + labels	π/6, π/4, π/3, π/2, π marked

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Assets & Dependencies

• Fonts: LaTeX
• Colors: SIN_COLOR = RED, COS_COLOR = BLUE_B, POINT_COLOR = WHITE, ANGLE_COLOR = YELLOW, BG = #1a1a2e
• Manim version: ManimCE 0.19.1

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Notes

• Unit circle drawn with radius=1 in Manim units scaled to the axes
• Wave graph x-axis represents θ from 0 to 2π
• Use ParametricFunction or dot-tracing to draw the waves incrementally
• always_redraw for the moving point, sin line, cos line, and angle arc