Vault Of Euclid

Vertical Tangents of a Parametric Curve

Parametric equations and vector functions core

For \( x = \sin(2t), y = 2 \sin t \) where \( 0 \le t < 2\pi \). Find all values of \( t \) at which a vertical tangent line exists.
parametric-equationsvertical-tangentderivativeschain-ruletrigonometric-equationscalculus-iicurve-sketchingtangent-linessinecosinefind-tangent

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What this problem tests

Tests the ability to compute derivatives of parametric equations and solve trigonometric equations to find specific geometric features of a curve.

This problem is typical of a Calculus II or Multivariable Calculus course when introducing calculus with parametric equations.

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