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Slope and Concavity of a Parametric Curve Involving Secant and Tangent

Parametric equations and vector functions core

Find the slope and concavity for the curve whose equation is \(x = 2 + \sec \theta, y = 1 + 2 \tan \theta\) at \(\theta = \frac{\pi}{6}\).
parametric-equationsderivativesslopeconcavitysecond-derivativetrigonometric-functionschain-rulecalculus-iievaluate-derivativefind-concavitysecanttangent

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What this problem tests

Tests the ability to apply the formulas for the first and second derivatives of parametric equations and to simplify trigonometric expressions.

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

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