For problems 14 – 27 sketch the graph of the given polar equation. 14. –7 = r sin 0 15. 0 = 7 16. 0 5 17. r cos 0 = 4 18. r = 6 sin 0 19. r = 100 20. r = 24 cos 0

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: After finding all the required values, for the polar curve r (0) : sin(0) we can find dy 2 -7 when 0…

A: FOR THE GIVEN INFORMATION

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation r = 2+ 3 sin…

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Q: Solve the problem. Te 1) Plot the point 2, and find other polar coordinates (r, 0) of the point for…

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

A: We solve it by following method.

Q: 2. r = 02, 0 < 0 < 3n

A: you can clearly understand if you follow the below solution

Q: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

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Q: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. r = 2 + 3…

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Q: Q3 Write down the polar form of the equation 2 arctan(y/a)

A: convert the given equation into polar form x2+y2=e-2arctanyx

Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 and equal 1/6 to 1/2 at increments…

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Q: 1 2 3 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A: Solve it.

Q: Write the equation (2² + y²)² = 10 xy in polar coordinates. a) Or? = 10 cos(2 0) b) Or? = 10 sin(0)…

A: We know that For conversion to polar form from cartesian equation. x=rcosθ y=rsinθ  Put these values…

Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Topic  = Derivatives

Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

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Q: 59. y = -3 cos 27.x + 2

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: The polar equation is r=2+3sinθ. Recall that fact that x=rcosθ,y=rsinθ. That is,…

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: Question 17 D The length of the curve y = sinI from I 0 to r 37/4is given by %3D 3x/4 sin rdr 3/4 B…

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Q: Match the graph with its polar equation. r = 3 (1 + cos(0)) T/2 1/2 4| -2 2 4 -2 -2 л/2 T/2 3- 2 1…

A: Topic :- Geometry As per our guidelines , In case of multiple different questios ,at a time only one…

Q: Q3 Check the symmetry and graph the curve in polar form if 0 = 0 to z at increments π/6(30°) use a…

A: Given curve r=(1+cosθ)----(1) The objective is to check the symmetry and graph the curve in polar…

Q: Q5/ Change the polar equation 2r = 2 + cos 0.(2r-1) to Cartesian equation Ans./y²-3x² - 4x-1=0

A: To find- Change the polar equation 2r = 2 + cosθ·2r - 1 to Cartesian equation.

Q: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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Q: Find the exact length of the polar curve

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Q: Find the slope of the line tangent to the following polar curve at the given point. 3π r= 5-5 sin 0;…

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Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…

A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given:

Q: 1 2 3 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A: For first condition ,  (2, 3pi/4)

Q: 21. r = -15 sin 0

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Which of the following shows the correct sketch of the polar curve r= -2 cos(3 0) for 0 <0 < ? 10 -…

A: Use Desmos graphing calculator. Option (b) is correct.

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

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Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: Which of the following Polar equation represents the following Curve -2 1 2 (a)r = 1 – sin® (b) r =…

A: A detailed solution is given below.

Q: aluate the dnd to polar

A: Given that, ∫0a∫02a-x2xx2+y2dxdy Take x=rcosθ, y=rsinθ where 0≤θ≤2π.

Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

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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: Given,  r=9+2 cosθ

Q: Find the equation in xx and yy for the line tangent to the curve in polar coordinates…

A: Given that, the value of r=5+cos2θ and θ=π3. rθθ=π3=5+cos2π3=5+-12=92 Note that, the equation of the…

Q: Which of the following shows the correct sketch of the polar curve r = -8 + 8 sin(0)?

A: The given polar equation is: r=-8+8sin(θ)

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: QUESTION 13 dx Given that r cos 0; dy = cos 20. de - sin 20 and de The slope of the tangent line to…

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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: 2. x = 3cos? (t) – sin? (t) y = 6 + cos(t) <t<0 2 - |

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Q: Which of the following shows the correct sketch of the polar curve r = 9 – 9 cos(0)?

A: We have to do following steps to solve it.

Q: For the polar equation r = 4+ 2 sin 0 :

A: We have r=4+2sinθ A graph is symmetric about x-axis if rθ=r-θ A graph is symmetric about y-axis if…

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

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Q: Match the graph with its polar equation. r = 2 sin(0) A/2 A/2 4 2 -2 2 4 - 2 2 - 4 A/2 3| л/2 2 1 1…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.