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Lesson: Finding the Slope of a Polar Curve

Worksheet • 25 Questions

Q1:

Find the points at which π‘Ÿ = 4 πœƒ c o s has a horizontal or vertical tangent line.

  • AHorizontal tangents at ( 2 √ 2 , πœ‹ 4 ) and ( 2 √ 2 , βˆ’ πœ‹ 4 ) , vertical tangents at ( 4 , 0 ) and ( 0 , πœ‹ 2 )
  • BHorizontal tangents at ( 4 , 0 ) , no vertical tangents
  • CHorizontal tangents at ( 4 , 0 ) and ( 2 √ 2 , πœ‹ 4 ) , vertical tangents at ( 0 , πœ‹ 2 ) and ( 2 √ 2 , βˆ’ πœ‹ 4 )
  • DHorizontal tangents at ( 4 , 0 ) and ( 2 √ 2 , βˆ’ πœ‹ 4 ) , vertical tangents at ( 0 , πœ‹ 2 ) and ( 2 √ 2 , πœ‹ 4 )
  • ENo horizontal tangents, vertical tangents at ( 4 , 0 ) and ο€» 0 , πœ‹ 2 

Q2:

Given a polar curve defined by π‘Ÿ = 𝑓 ( πœƒ ) , form an expression for the slope of the curve d d 𝑦 π‘₯ in terms of πœƒ and 𝑓 .

  • A d d s i n c o s c o s s i n 𝑦 π‘₯ = 𝑓 β€² ( πœƒ ) πœƒ + 𝑓 ( πœƒ ) πœƒ 𝑓 β€² ( πœƒ ) πœƒ βˆ’ 𝑓 ( πœƒ ) πœƒ
  • B d d s i n c o s c o s s i n 𝑦 π‘₯ = 𝑓 ( πœƒ ) πœƒ + 𝑓 β€² ( πœƒ ) πœƒ 𝑓 ( πœƒ ) πœƒ βˆ’ 𝑓 β€² ( πœƒ ) πœƒ
  • C d d s i n c o s c o s s i n 𝑦 π‘₯ = 𝑓 β€² ( πœƒ ) πœƒ + 𝑓 ( πœƒ ) πœƒ 𝑓 β€² ( πœƒ ) πœƒ + 𝑓 ( πœƒ ) πœƒ
  • D d d c o s s i n s i n c o s 𝑦 π‘₯ = 𝑓 β€² ( πœƒ ) πœƒ βˆ’ 𝑓 ( πœƒ ) πœƒ 𝑓 β€² ( πœƒ ) πœƒ + 𝑓 ( πœƒ ) πœƒ
  • E d d s i n c o s c o s s i n 𝑦 π‘₯ = πœƒ + πœƒ πœƒ βˆ’ πœƒ

Q3:

Find the slope of the tangent line to π‘Ÿ = πœƒ at πœƒ = πœ‹ 2 .

  • A βˆ’ 2 πœ‹
  • BThe slope of the tangent line is undefined.
  • C 2 πœ‹
  • D1
  • E βˆ’ πœ‹ 2
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