Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 6, Problem 12SP
To determine
To find: The point of intersection of the polar curves
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37. The Cartesian equation of the polar curve
2 = 2a' sin 20 is
A. 1? + y? = 4a²xy
B. (z* + 3° )° = a°zy
C. a? + y? = 4xy
D. (z? + y² )° = 4a²zy
4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to
indicate the orientation of the graph.
YA
10
x=4+cos(0) , y=-1+sin(0)
-9 -8-7 -6 -5
4-3 -2 -10
4 56 7 8 9 10
х
-1
-2
-3
-5
-6
-7
-9
13. r² = a¹ sin 20
r=a(1+cos 6)
How many of these 5 equations in polar form have graphs that are symmetric with
respect to either the x-axis or the y-axis (or both axes)?
(a) one (b) two (c) three (d) four (e) five
rsin0 = 3 r=4 cos 30
2/0
Chapter 6 Solutions
Calculus
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.arrow_forward4. Find the exact length of the polar curve r = e2θ, 0 ≤ θ ≤ 2π.arrow_forward2 3. If tan(a-iß) = x-iy, show that x² + y° - 2ycoth2B = -1 -1arrow_forward
- 3. You want to manufacture a fruity cake in a unique shape. You designing a shape for a fruity cake by generating r=8 sin 0 – 2 sin 40 about the polar axis and make it 8 cm in height. You decide to pack it in a box. You need to know how much mixture of fruity cake to have on hand for a production run of ten boxes. Sketch the graph of r.arrow_forwardabcoso. (b) The length in first quadrant of the curve x²/3 + y²/3 = a²/3 is given by 6ac/2 where %3D parametric equations of curve are x = a cos 8,y = a sin 0. Compute the value of c. Also find the length in first quadrant of the curve (x/a)?/3 + (y/b)*/3 =1 where parametric equations of curve are x = a cos 0, y = b sin*e.arrow_forwardPLEASE PLEASE DRAW THE GRAPH!!!!!!! solve only 3arrow_forward
- 3Q. If z₁ = (cos50 – i sin 50), z₂ = (cos70 + i sin 0) and z3 = (cos40 – i sin 40) then find Z3 polar form. .9arrow_forward-8 But Draw the graph of the parametric curve defined by x(t) = 6 cos(t) and y(t) = 6 sin(t) below. 6 S 4 3 2 + √6 5 4 3 2 -4 j -2 -3 4 --5- -6 -7 8 1 2 3 4 5 6 7 8 -6+ Clear All Draw: /AVO • Question Help: Message instructorarrow_forwardshow accurate solution for 1 and 2..arrow_forward
- 10.3.63 Convert the Cartesian equation to a polar equation that expresses r in terms of 0 (x- 6) +y? = 36 (Type an expression in terms of 0.)arrow_forward1. Match each equation in rectangular coordinates with its equation in polar coordinates: (a) x² + y² = 4 O r²(1-2 sin² 0) = 4 r(cos 0 + sin() = 4 r = 2 sin 0 Or=2 (b) x² + (y − 1)² = 1 O r²(1-2 sin²0) = 4 r(cos+ sin 0) = 4 r=2 sin 0 r = 2 (c) x+y=4 Or² (1-2 sin² 0) = 4 r(cos+ sin 0) = 4 r = 2 sin 0 Or=2arrow_forward6.) Use your calculator to make a graph of the polar function r(0)=2sin (0) - cos (30) on the grid shown, where 0≤0≤180°, by first filling in the table below. Round the values in the table to the nearest tenth. Shown are the standard angles and radii of 1, 2 and 3 to help. 0 r 0 r R 0° 120° 30⁰ 135° A 45° 150⁰ The T weather 60⁰ 180° F7 90° F8 F9 F10 F11arrow_forward
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