Parametric Equations and slope

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SUMMARY

The discussion focuses on finding points on the parametric equations defined by x=4cos(t) and y=4sin(t) that yield a slope of 1/2. The derivative dy/dx was calculated as -cot(t). To solve for the required points, one must set -cot(t) equal to 1/2 and solve for the parameter t. It is clarified that the given parametric equations represent a single curve rather than multiple curves.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of derivatives and slope calculations
  • Familiarity with trigonometric functions, specifically cotangent
  • Basic algebra skills for solving equations
NEXT STEPS
  • Learn how to derive parametric equations and their slopes
  • Study the properties of trigonometric functions, particularly cotangent
  • Explore the graphical representation of parametric curves
  • Practice solving equations involving trigonometric identities
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Students studying calculus, particularly those focusing on parametric equations and derivatives, as well as educators seeking to enhance their teaching methods in these topics.

reconrusty
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Homework Statement


Find all the points on the following curves that have the given slope:

x=4cost
y=4sint
slope=1/2

Homework Equations

The Attempt at a Solution


Im not to sure what to do with this question.. I found dy/dx to be -cot(t) but I am not sure if that is even needed for this problem. Any help would be greatly appreciated !
 
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reconrusty said:

Homework Statement


Find all the points on the following curves that have the given slope:

x=4cost
y=4sint
slope=1/2

Homework Equations

The Attempt at a Solution


Im not to sure what to do with this question.. I found dy/dx to be -cot(t) but I am not sure if that is even needed for this problem. Any help would be greatly appreciated !
That's a good start. Now just set -cot(t) = 1/2 and solve for t.

BTW, your parametric equations represent one curve, not multiple curves.
 

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