Vault Of Euclid

Horizontal and Vertical Tangents of a Parametric Curve

Parametric equations and vector functions core

Find all points on the curve \( x = \sec \theta, y = \tan \theta \) at which horizontal and vertical tangents exist.

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Derivatives of trigonometric functions
Solving basic trigonometric equations
Understanding of parametric equations

What this problem tests

Tests the ability to compute derivatives of parametric equations and solve trigonometric equations to find specific tangent line behaviors.

This problem is typical in a Calculus II course when introducing calculus with parametric equations.

More on Parametric equations and vector functions

Arc Length of a Polar Circle warmup
Solving a Separable First-Order Differential Equation warmup
Highest Point of a Parametric Curve warmup
Arc Length of a Parametrized Circle warmup
Distance Traveled by a Particle on a Parametric Curve core
Solving a Simple Separable Differential Equation warmup

← today's set