Vault Of Euclid

Arc Length of a Parametrized Circle

Parametric equations and vector functions warmup

Find the arc length of the circle parametrized by \( x = 3 \cos t \), \( y = 3 \sin t \) on \( [0, 3\pi/2] \).

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What you need first

derivatives of sine and cosine
the Pythagorean trigonometric identity
evaluating definite integrals of constants

What this problem tests

Tests the ability to apply the parametric arc length formula and simplify trigonometric integrands.

This is a standard introductory problem in Calculus II or Multivariable Calculus when learning about calculus with parametric curves.

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Distance Traveled by a Particle on a Parametric Curve core
Solving a Simple Separable Differential Equation warmup

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