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Identity in Motion: Using sin²θ + cos²θ = 1 to Validate Robotic Arm Design
Identity in Motion: Using sin²θ + cos²θ = 1 to Validate Robotic Arm Design
How can we use sine and cosine to locate the robot arm tip precisely at any angle?
Learning Intentions:
Build the unit circle from robot measurement data and identify that the x-column represents cosine and the y-column represents sine, including the Pythagorean identity.
Today's Concept:
Set your robot arm to 30°. Where exactly does the tip end up? Not approximately — exactly. The formulas x = r·cos(θ) and y = r·sin(θ) answer that question for any angle.
You won't start with the formulas today. You'll generate the data yourself by measuring the tip's x and y position at four different angles. The pattern in your numbers will reveal the unit circle — and something else: for every row you measure, x² + y² equals r². That identity holds for every angle, every time. It's called the Pythagorean identity, and your own data proves it.
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Explore It - Pythagorean Identity
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