4. (a) What is the composition of a 90 degree rotation about the origin, followed by a 90 degree rotation about (1,0)? (b) What is the composition of a 90 degree rotation about the origin, followed by the reflection across the line x=y?

Q: 4) 4+ 3+ -5 -4 -3 -2 3 4 5 r -2+ -3+ -4+ 2.

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Q: 4. (a) Plot the following points in the same polar coordinates system (b) Convert into rectangular…

A: To convert the polar coordinates r,θ to rectangular coordinates x,y then x=rcosθ and y=rsinθ

Q: Use a graphing utility to convince yourself that the polar equations r = f1(θ) = 2 cos θ − 1 and r =…

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Q: 6. (3+ 2j)/(4 – 7j) 7. Convert -5 – 7j to polar form.

A: 6. Given(3+2j)/(4-7j) Rewrite the above equation as: (3+2j) (4-7j)× (4+7j) (4+7j) =(3+2j)(4+7j)…

Q: Find the image of (2, –2) after a clockwise (active) rotation about the origin by an angle 0 = 1/4.…

A: Find the image of (2,-2)?

Q: TRUE OR FALSE. The polar equations r = cos 3θ -2 and r = 2-cos 3θ represent the same graph.

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Q: Write polar form of z=-2-i V5 (cos2.68 + i sin2.68) 5(cos2.68 – i sin2.68) V5(cos2.68 – i sin2.68) 5…

A: We are given the complex number : z=-2-i=x+iy⇒r=-22+(-1)2=5tan θ=-1-2=12Now, x=r cos θ<0and y=r…

Q: The Cartesian coordinates of a point are given. (a)     (−9, 9)   (i) Find polar coordinates  (r,…

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Q: An equation whose variables are polar coordinates is called a(n)...............…

A: given,        An equation whose variables are polar coordinates is called a(n). . . . . . . . .…

Q: 2. Give 3 other representation of the polar coordinate (changing the sign of r at least once). (2)

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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: Plot each ordered pair written in polar coordinates below, and then find a new polar coordinate…

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

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Q: 1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. (make it as an…

A: Given:  Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0