Trigonometric Functions on a Scaled Grid

Overview

A visual comparison of the three basic trigonometric functions $y=\sin\ heta$, $y=\cos\ heta$, and $y=\ an\ heta$ plotted on a common grid with a custom angular and vertical scale. The viewer sees the characteristic shapes, peaks, zeros, and asymptotes, reinforcing the relationship between angle and function value.

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Phases

#	Phase Name	Duration	Description
1	Intro	~2s	Fade‑in of a blank grid board; brief pause before drawing axes.
2	Draw Axes & Scale	~4s	Draw x‑axis and y‑axis lines, add tick marks. Apply the scale: 2 cm = 30° on the x‑axis and 2 cm = 0.5 units on the y‑axis. Label the axes with degree markers (0°, 30°, …, 360°) and unit markers (‑1, ‑0.5, 0, 0.5, 1).
3	Plot $y=\sin\ heta$	~6s	Using a blue pen, trace the sine curve from 0° to 360° following the described points (0,0) → (90°, +1) → (180°, 0) → (270°, ‑1) → (360°, 0). End with a small persistent label "$y=\sin\ heta$" in blue near the end of the curve.
4	Plot $y=\cos\ heta$	~6s	Using a red pen, trace the cosine curve starting at (0°, +1) and proceeding through the same angular range, matching the described points. Conclude with a red label "$y=\cos\ heta$".
5	Plot $y=\ an\ heta$	~8s	Switch to a green pen. First draw vertical dashed lines at 90° and 270° to indicate asymptotes. Then plot the tangent in three segments: (0°, 0) → (30°, ≈0.58) → approach the 90° asymptote; segment between 90° and 270° emerging from the bottom left, crossing (180°, 0) and heading toward the 270° asymptote; final segment from just right of 270° up to (360°, ≈0). Finish with a green label "$y=\ an\ heta$".
6	Outro	~2s	Slight pause, then fade‑out of the entire scene.

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│                MAIN (graph)                 │
│                                             │
├─────────────────────────────────────────────┤
│  Caption (optional) – can show current curve │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	Grid board with axes, tick marks, and the three plotted curves (blue sine, red cosine, green tangent).	Uses the custom scales; all visual focus is here.
Caption	Small persistent text indicating which curve is being drawn (e.g., "Plotting $y=\sin\ heta$").	Appears only during the corresponding plotting phase; disappears afterward.

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Notes

• Assumptions: No explicit request for titles or legends, so only minimal captions are used during each plotting phase. The grid is centered with the origin at the left‑most bottom of the visible area to accommodate the full 0°–360° range.
• The vertical scale is limited to $[-1.5, 1.5]$ to comfortably display the sine and cosine peaks and the tangent’s near‑asymptotic behavior without clipping.
• Dashed asymptote lines are drawn in a light gray color to keep focus on the green tangent curve.
• All animations use smooth linear or sinusoidal easing to convey natural motion of the curves.
• The entire specification is designed for a single Manim Scene class.