tr11-2 - Section 11.2 Tangent lines and arc lengths for...

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Section 11.2 Tangent lines and arc lengths for parametric & polar curves Learning outcomes After completing this section, you will inshaAllah be able to 1. learn how to find slopes and tangent lines of parametric curves 2. learn how to find slopes and tangent lines of polar curves 3. know special trick to find tangent line to polar curves at pole 4. find arc length of polar curves 1 11.2
Tangent lines to parametric curves Given a parametric curve ( ), ( ); x f t y g t a t b = = dy dx is defined when 0 dx dt and dy dy dt dx dx dt = Similarly 2 2 d dy dt dx d y d dy dx dx dx dx dt = = Example 11.2.1 Consider the parametric equation 2 3 , 3 x t y t t = = . Find 2 2 , dy d y dx dx at 1 t = . Solution Done in class 2 11.2 À slope of tangent line at 0 0 ( ), ( ) x f t y g t = = 0 t t dy dx = À Tangent horizontal when 0 and 0 dy dx dt dt = À Tangent vertical when 0 and 0 dx dy dt dt = À Points where 0 and 0 dy dx dt dt = = are called singular points

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