Calculus with Parametric Curves For the curve defined by the parametric equations[x = 3 + secty=3+5 tantFind the first derivative:dydr5 sec² (t)sec (t) tan(t)Find the second derivative:d'y= 5 cot³ (t)X3πDetermine whether the curve is concave up or concave down at t =4-: Concave up

The given parametric equation of curve is

For the curve defined by the parametric equations [x = 3 + sect y=3+5tant Find the first derivative: dx 5 sec²(t) sec (t) tan(t) Find the second derivative: d²y dx² 5 cot" (t) X 3π Determine whether the curve is concave up or concave down at t = 7 -: Concave up

For the curve defined by the parametric equations [x = 3 + sect y=3+5tant Find the first derivative: dx 5 sec²(t) sec (t) tan(t) Find the second derivative: d²y dx² 5 cot" (t) X 3π Determine whether the curve is concave up or concave down at t = 7 -: Concave up

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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Question

Calculus with Parametric Curves

For the curve defined by the parametric equations
[x = 3 + sect
y=3+5 tant
Find the first derivative:
dy
dr
5 sec² (t)
sec (t) tan(t)
Find the second derivative:
d'y
= 5 cot³ (t)
X
3π
Determine whether the curve is concave up or concave down at t =
4
-: Concave up

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Step 4: Calculate the concavity

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