18. r = cos"/3' 19. r = cos 20, 0 = "/a

Q: 2. In both parts, full marks will only be obtained if exact answers are given in terms of . √2 etc.…

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Q: 3. Draw the polar curve r = 3 +sin 30

A: Solution: The objective is to graph the polar curve r=3+sin(3θ)

Q: Convert the cartesian coordinate (-6, – 1) to polar coordinates, 0 < 27

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Q: A curve with polar equation r=48/6sinθ+25cosθ represents a line. This line has a Cartesian equation…

A: Given that, the polar equation is r=486sinθ+25cosθ. Convert the polar equation as Cartesian equation…

Q: The curve with polar equation 24 3 cos 0 + 4 sin 0 = s a line. Find the slope and the y-intercept of…

A: We will have to covert the polar equation 3cosθ+4sinθ=24r in Cartesian form. Also, we will have to…

Q: 3. Find two different sets of polar coordinates (r. 8) for the point with Cartesian coordinates (x,…

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Q: For Cartesian coordinates (x,y)=(1, -√3), find the angle in the polar coordinates in radians.

A: Use the formula for angle in the polar coordinates.

Q: A family of curves has polar equations  ra  =  ∣ sin 2θ∣ where a is a positive number. Investigate…

A: The equation of the family of curves is ra=sin2θ, where a is a positive number. We need to visualize…

Q: Let c be a fixed constant. Explain the relationship betweenthe graphs of: r = f (θ + c) and r = f (θ…

A: Given that: “c” be a fixed constant r=fθ+c      and       r=fθ                      Polar

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

A: To draw a polar graph we need to check its symmetricity by using following   #  In the first test,…

Q: Sketch with direction of the following functions r = f(θ) in polar coordinate. please sketch with…

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

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Q: ecified by the val COS 3

A: The slope of a polar curve r=fθ is given as follows. dydx=dydθdxdθ=fθ cosθ+f'θ sinθ-fθ sinθ+f'θ cosθ…

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: Do a complete analysis to determine the points of intersection of the polar curves r = 4 sin 0 and…

A: We need to find the points of intersection. So,              4sinθ=1+2sinθ⇒sinθ=12⇒θ=π6+2πn,…

Q: Find the polar equation for the Cartesian curve x² = Or= Or T = Or= Ora 1 Or= -tan 0 2 1 2 1 sin 0…

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Q: Convert the rectangular coordinate point (2,-2) to polar coordinate.

A: To convert into polar coordinates

Q: Without using a calculator, for the following, find rectangular coordinates for the given point in…

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Q: Ship X left the harbor at a speed of 25 n.m/hr Northeast while Ship Y is already in the ocean at…

A: We will draw diagram and then use co ordinate and trigonometry tp find required values

Q: 7) Find the points at which the polar curve r = 1+ cos® have horizontal or vertical tangent lines.

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