20 4. An ant walks on a flat surface along a curve with polar equation r= from a point where 0=0 to another point where 0= 27 rad. (a) Calculate the values of r for 0 equals to 0,. 7. 3 and 27 radians, and hence make a sketch of the trajectory of the ant. (b) Determine the total distance travelled by the ant.

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: 24. A particle moves round the polar curve r = a(1+ cos e) with constant angular velocíty w. The…

A: We have constant angular velocity = w  r = a(1+ cosθ)

Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

A:

Q: 5. [10pts] Compute the arclength of the polar curve r = 2° for 0 < 0 < 27. Give both the exact…

A: Find the arc length of polar curve

Q: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (38), e…

A:

Q: 4 Find the slope of the tangent line to polar curve r = 7 – 4 sin 0 at the point ( 7 - - 2' 6 Submit…

A:

Q: 6. Consider the curves: r = 2 + cos 2θ and r = 2 + sin 2θ, a) Sketch a graph of both curves on the…

A:

Q: A particle moves along the polar curve r = -4+ 4 sin 0 in such a way that the angle between the…

A: r = -4+4sinθ  dθ/dt= 5 unit/sec  Find dr/dt when θ = π/2

Q: 36 A curve with polar equation r = 29 sin 0 + 7 cos 0 represents a line. Write the equation of the…

A:

Q: 5/3 Convert the point with Cartesian coordinates 2 to polar coordinates. Enter exact values for r…

A: Convert the point with Cartesian coordinates 52,-532 to polar coordinates.Enter exact values for r…

Q: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

A:

Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sin0 -3cos0+1 at 0= 1/4

A: Using slope formula we have

Q: 12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values o for…

A:

Q: 6. Consider the curves: r = 2+ cos 20 and r = 2+ sin 20, a) Sketch a graph of both curves on the…

A:

Q: (b) Find the slope of the line tangent to the polar curve r = 1- 2 cos e at the point where e = -2.…

A:

Q: 9. (a) Find the rectangular coordinates of the point(s) of the graph of the polar equation r = 4 sin…

A:

Q: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

A:

Q: 67. r 3D сos 2ө, ө — п/4

A:

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

A:

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

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

A:

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 5 cos(6) 2

A: To find the length of curve

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

A: The given polar equation is r=2-sin2θ. Draw the graph of the given polar equation in detail.

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Solve by finding slope

Q: 33 A curve with polar equation r 9 sin 0 + 55 cos 0 mx + b,where m and b are represents a line. This…

A:

Q: 44 A curve with polar equation r = 7 sin 0 + 36 cos 0 represents a line. This line has a Cartesian…

A:

Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2

A:

Q: Q/ sketch r:2 sinlo -)cos(0-) in polar system. ExPlav e is the graphic symme trical and wribing a…

A:

Q: The curve (x-)*+Cy +1)*= 4, x 7,1 is given. First draw it in the Cartesian plore and then transtorm…

A:

Q: 10. Consider the curve with polar equation r = 6 sin 0 where 0< 0 <T. WVithout finding the Cartesian…

A:

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and the…

A:

Q: Find the points at which the polar curve r= 5+ 10 sin 0 has a horizontal or a vertical tangent line.…

A: the equation of the given curve in polar form is: r=5+10sinθ we have to find the points to the curve…

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

A:

Q: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

Q: 44. The furthest point from the pole to the polar curve r = 2+ V2 sin 0 occurs when 0 = A. в о C 2

A: Answer

Q: (iii) 3rd subplot is A butterfly curve using polar coordinates: 2a - I r = esina – cos(4a) - sin( 24…

A: (iii) Matlab Code: clc; clear all; close all; theta= 0 : pi/32 : 8 * pi; r= e.^…

Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

Q: 2. Determine the area of the region that is simultaneously interior to the curve r = 2 + cos (30), e…

A: Given that, An area is simultaneously interior to the curve r=2+cos3θ, and exterior to the curve…

Q: 8/3 Find the slope of the tangent line to polar curve r = 8 sin 0 at the point 3.

A: Explanation of the answer is as follows

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: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

A:

Q: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: 7 A curve with polar equationr = 5 sin 0 + 31 cos 0 represents a line. This line has a Cartesian…

A: topic - change in coordinate system

Q: 3. Determine the arc length of the polar curve r= 2-2 sin0.

A: Given: r=2-2 sin θ   ……1

Q: 23 A curve with polar equation r : 4 sin 0 + 13 cos 0 represents a line. This line has a Cartesian…

A:

Q: 7) Sketch the polar curve r = 2(1+ sin 0). In your graph, label the points corresponding to the…

A: We have to find out the graph and points according to value of θ