sin-unit-circle-animation

name	sin-unit-circle-animation
description	Create animations showing the Unit Circle → Sine Wave connection. Uses ValueTracker + always_redraw for smooth rotating point that traces out the sine wave. Perfect for educational content (11th grade math, trigonometry).
version	1.0.0

Unit Circle → Sine Wave Animation

When to Use

Create animations showing the Unit Circle → Sine Wave connection. Uses ValueTracker + always_redraw for smooth rotating point that traces out the sine wave. Perfect for educational content (11th grade math, trigonometry).

Overview

This skill contains a reusable operational workflow. Follow the existing task-specific steps and examples in the sections below.

Core Approach

The key pattern: use ValueTracker + always_redraw for smooth, real-time animation of a rotating point on a unit circle, where the y-coordinate traces out a sine wave.

Why ValueTracker + always_redraw?

• Smooth animation — Manim interpolates the ValueTracker smoothly over the run_time
• Automatic synchronization — point position, radius line, wave, and projection line all update together
• No manual frame building — avoids fragile manual VMobject point arrays
• Clean code — all dependencies expressed as always_redraw lambdas

Step-by-Step

1. Set up ValueTracker for angle

theta = ValueTracker(0)  # θ starts at 0 radians

2. Create always_redraw mobjects

point = always_redraw(lambda: Dot(
    2 * np.array([np.cos(theta.get_value()),
                  np.sin(theta.get_value()), 0]),
    color=GREEN, radius=0.08
))

radius = always_redraw(lambda: Line(ORIGIN,
    2 * np.array([np.cos(theta.get_value()),
                  np.sin(theta.get_value()), 0]),
    color=YELLOW, stroke_width=2))

arc = always_redraw(lambda: Arc(radius=0.5, start_angle=0,
    angle=theta.get_value(), color=ORANGE, stroke_width=2))

3. Build the sine wave (also driven by ValueTracker)

wave_points = ValueTracker(0)  # 0 to 1 controls how much wave is revealed

def build_wave():
    n_points = 200
    max_t = wave_points.get_value() * 2 * PI
    pts = []
    for j in range(int(n_points * max_t / (2 * PI)) + 1):
        t = j * 2 * PI / n_points
        x_w = wave_origin[0] - 0.5 + j * 7.0 / n_points
        y_w = wave_origin[1] + 2 * np.sin(t)
        pts.append([x_w, y_w, 0])
    wm = VMobject()
    wm.set_points_as_corners(pts)
    wm.set_color(GREEN).set_stroke(width=4)
    return wm

wave_reveal = always_redraw(build_wave)

4. Animate both together

self.play(
    theta.animate.set_value(2 * PI),
    wave_points.animate.set_value(1),
    run_time=8,
    rate_func=linear,
)

Common Pitfalls

Pitfall	Fix
Using run_time(...) instead of run_time=	Always keyword: run_time=8
DOWN_RIGHT doesn't exist	Use RIGHT * 2 - DOWN * 1.5
MathTex with font= parameter	Use MathTex().scale() instead
MathTex.get_part_by_tex() returns None	Use set_color_by_tex()
ParametricFunction with t_min/t_max	Use t_range=(min, max, step)
Manual VMobject point building	Use always_redraw + ValueTracker
get_part_by_tex() returns None	Use set_color_by_tex()
MathTex with font parameter	Use .scale() instead

Color Palette (Dark Background)

BG       = "#0D1117"
GREEN    = "#83C167"   # E field, sin wave, positive
BLUE     = "#58C4DD"   # B field, secondary
YELLOW   = "#FFFF00"   # highlights, radius
ORANGE   = "#FF9F43"   # angle θ
PURPLE   = "#C792EA"   # propagation, tertiary
WHITE_C  = "#EAEAEA"   # body text
DIM      = "#7A8599"   # axes, labels
RED      = "#FF6B6B"   # negative slopes, warnings

Pacing

Section	Timing
Title	1.5s
Circle + axes appear	0.7s
Point, radius, arc, labels	1.2s
Wave frame appears	0.9s
Rotation + wave build	8s (linear)
Equation	2.1s
Final note + fade	1.9s
Total	~16s

Verification Checklist

• ValueTracker for angle and wave progress
• always_redraw for all dependent mobjects
• theta.animate.set_value(2*PI) synchronized with wave building
• run_time= keyword (not function call)
• set_color_by_tex() for MathTex coloring (not get_part_by_tex())
• No DOWN_RIGHT or other non-existent direction shortcuts
• ParametricFunction uses t_range= tuple, not t_min/t_max
• MathTex uses .scale() not font_size parameter