19. Which of the following polar functions is a limacon with dent?A) r= 2+2 cos 0B) r= 2+5 cos 0C) r= 5+3 cos 0D) r= 4+2 cos 0

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Answered: 19. Which of the following polar…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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( Back Analytic Geomet 17 of 19 Convert the following function given in Cartesian Coordinates into Polar form. * = V25 – y? 25 O r= cos? 0 – sin? 0 25 Or = cos? 0 + sin? 0 O r = 5 Or= cos 8 – sin 0 evious 2059%23 MAY 13 MacBook Pro
Solve this:
2. Write +i tan A in polar/trinometric form r(cos 0+ i sin 0) or re" or r Z0.
4. Consider the polar curves C₁ r = 2 sin and C₂ : r = 2 cos 0, where 0 ≤0 ≤ 2T. a) Find the Cartesian equations of C₁ and C2 and make a neat sketch of these curves. b) Using polar equations of C₁ and C2 to find their intersection points (Do not use their Cartesian equations!). c) Using polar equations of C₁ and C₂ to show that they intersect each other at right angles (Do not use their Cartesian equations!).
3Q. If z₁ = (cos50 – i sin 50), z₂ = (cos70 + i sin 0) and z3 = (cos40 – i sin 40) then find Z3 polar form. .9
See the pic please (5)
1. The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, 0). x2+ 4y 2 - 4 O 4 cos2 e + sin? e - 4r O p2(4 cos² e + sin² ®) = 4 O cos2 8 + 4 sin² e = 4r O 2(cos² e ®) = 4 + 4 sin? e 18 Match the graph to one of the polar equations. O r= 2 cos e O sin 8 = 1 Or= 2 sin 8 Or= 1
Steps to Sketching the Sinusoidal Functions: 1. Lightly sketch the midline line y = D. The midline "splits" the graph into upper and lower halves. 2. Lightly sketch the horizontal lines y=D+A and y = D-A. These two lines determine a horizontal strip inside which the graph of the sinusoidal function will oscillate. Notice, the points where the sinusoidal function has a maximum value lie on the line y = D + |A|. Likewise, the points where the sinusoidal function has a minimum value lie on the line y = D-|A|. 3. Lightly sketch the vertical lines at x = C and x=C+B. One cycle of the sinusoidal function will lie between these two lines. 4. Sketch one cycle of the sinusoidal function in the box created by steps 2 & 3. The important points (minimums, maximums, and crossing the midline) will B, C+B. occur when x= C, C+-B, x= C, C+ B, C+ B, C+ B₁C 4 2 4 a. Sine, A > 0: mid-max - mid - min - mid Sine, A 0: max - mid - min - mid - max Cosine A < 0: min - mid-max - mid - min 5. The fact that the…

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19. Which of the following polar functions is a limacon with dent? A) r= 2+2 cos 0 B) r= 2+5 cos 0 C) r= 5+3 cos 0 D) r=4+2 cos 0