Given that 2r +1= cos 0. i. Test the symmetries of the above equation. ii. Construct a table for (r, 0) where 0° < 0 < 2m with increment of and TM sketch the graph of 2r +1 = cos 0. (Use the polar grid provided) iii. Sketch the graph r + sin 0 = 0 on the same diagram. UNIVERSITI TEKNOLOGI MALAYSIA-

Q: Q7:- sketch the graph of the following polar equation. 3- r = 6 cos 6 1- 0 = 6. 5- r= 3(1- sin0) 2-…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Draw phe Polar curve defind by r=4+2 Cos 36

A: Given:

Q: 12/2 Use polar coordinates to evaluate dydx.

A: The region is bounded by x=1,x=2,y=0 and y=x

Q: 4-If y= cos 8t , find the frequency (w) and the fundamental period(T.) 5-If: y = (sinx+1) (cosx+1)'…

A: We know that, The fundamental period(T0) of cos(x) = 2.pi                            if cos(ax) = (…

Q: The area of one loop of the graph of the polar equation r =2 sin 30 is Select one: O27 3

A: r=2sin3θ

Q: 55. Find the polar coordinates of the points on the lemniscate r2 = cos 20 in Figure 24 where the…

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Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

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Q: Which of the following is an equation of the tangent line to the polar curve r = 2(1+cos 0) at the…

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Q: How many petals are there in the graph of the polar equation r = 2 cos3@ ?

A: Draw the polar curve

Q: What is the length of the polar curve below? = 2 cos(0) for 0 sos 4

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Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: 1. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: Find exact value of cos(2a) for the problem attached

A: Given

Q: Find the area A of the shaded region in the figure between the inner and outer loop of the limacon…

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Q: Sketch a graph of the polar equation r = 3 sin 2 and find the tangent line(s) at the pole (if any).

A: We have to sketch a graph of the polar equation r=3sin2θand then we have to find the tangent line(s)…

Q: Which of the following graphs represents the polar equation defined by: r = 2+2 cos 0?

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Q: Sketch and find additional polar three points for (2,4pi/3). When r&gt;0 and r&lt;0. And theta is…

A: Given polar coordinate:

Q: Find the equation of the following polar graph: 10 5- -10 -5 5n 10 -10 - a) Or = 2+4 cos(e) b) Or=…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 9 cos(8) 2

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Q: test for symmetry and graph polar equation

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Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is…

A:

Q: Consider the curves: r = 4sin 0 and r = 2 sin(0) + 2cos (8). a) Sketch a graph of both curves on the…

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Q: 5. If z = 2(cos 25° +j sin 25°), find z in polar form.

A: It is simple calculation in polar form

Q: Find the length of the curve over the given interval.                                     Polar…

A: Given: rθ=5cosθ; θ∈π2,π we know that arc lengthL for any given functionfx over interval a,b is given…

Q: 6. Find the area of one loop of the polar curve r = 2 sin 30

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Q: Find the smallest interval for θ starting with θ min = 0 so that your graphing utility graphs the…

A: Consider the given polar equation, r=4sin2θ use the Desmos graphing calculator to graph the…

Q: 2) Sketch the graph of the curve with the polar equation: r= 2– sin(20).

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Q: Which of the following shows the correct sketch of the polar curve r = 9 sin(3 0)? 10 -10 5 10 -5…

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Q: 1 8. Given that cos 0 and <0 < 2n, find the other circular functions. %3D

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Q: = 2/(1+ cos 0) and find its relevant parame Identify the curve r = Write an COS equivalent Cartesian…

A: We know that the Cartesian coordinate x,y of a points related to its polar co-ordinate r,θ is given…

Q: 4. Suppose that the final digits of your student number are . abcd if it is a 4 digit number or .…

A: As per the guidelines I am supposed to do the first 3 subparts only. Kindly repost the others…

Q: The area of one loop of the graph of the polar equation r = 2 sin 30 is Select one: IT 3 2 4 2n 3

A: Solve by definite integration

Q: 2. a. Sketch the graphs of the rose r = 4 cos20 and the circle r = 2 in one polar plane. Provide a…

A: Given: and   Formula used:

Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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Q: (D)y= cos C2x) E CCs (1) m'tm= o (2)

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Q: 6. Find the length of the polar curve r = 1+ cos 0 on the interval 0 < 0 < n.

A: Given:

Q: Q1 Find the points of intersection of the polar curves rcos and 2-cos 0-r=0

A: The value of the cosine function  cos0=1cosπ6=32cosπ4=12cosπ3=12cosπ2=0cosπ=-1cos3π=-1cos2π=1

Q: 1. Sketch the graph of r=1-cos in polar coordinates. [3 marks]

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Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…

A: We are given that,                     Now,              When          , Then

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 8a cos 0 16 16.

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Q: Sketch a graph of the polar equation r = 3 cos 4θ and find the tangent lines at the pole.

A: Given: The equation r=3 cos 4θ To sketch: The graph of the given equation. To find: The tangent…

Q: 5- Graph the polar curve given by: r=2 +4 cos 0. Give the range of 0 in which the inner loop is…

A: To  get the range of θ we need to check the when the curve r crosses through the origin

Q: Find the two square roots of z (call them wi and w2) and express in complex polar form r(cos(0) + i…

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Q: Given z1 = 5(cos 184° + i sin 184°) and z2 = 3(cos 271° + i sin 271°), find the following: 71 Z2=.…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: We have to find the slope of the tangent line to the polar curve  r = cosθ3 at the point θ=π.

Q: For what value of k does the polar graph r= ksine + 1 produce a horizontal tangent at 9-? Ok= 1…

A: We will solve the problem

Q: Find the slope of the polar curve at the indicated point. A) V3 r = 1- sin(0), 03= 3 C) 2

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Q: 40 cos*“for 0 < 0<m

A: