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Identify the polar coordinates for each value in the table below, discuss the shape and behavior of the graphs, and use this to graph the equation of r=2 cos⁡〖3θ.〗
Symmetry hint: see if the equation is true for the following:
the line θ = 90°: replace (r, θ) with (r, 180° – θ) or (-r, -θ)
the polar axis: replace (r, θ) with (-r, 180° – θ) or (r, -θ)
the pole: replace (r, θ) with (r, 180° + θ) or (-r, θ)

Identify the polar coordinates for each value in the table below discuss the shape and behavior of the graphs and use this to graph the equation of r2 cos3θ Sym class=

Respuesta :

1Marshmello

Answer:

we know that

the relationship between the 2-dimensional polar and Cartesian coordinates is

r = √(x² + y²)

Θ = tan⁻¹ (y/x)

so

Part a) (2, −2)---------> this point belong to the IV quadrant

r = √(x² + y²)------ r = √(2² + (-2)²)-----> r=√8

Θ = tan⁻¹ (y/x)---- Θ = tan⁻¹ (2/2)----> 45°

remember that the point belong to the IV quadrant

so

Θ=360-45-----> Θ=315°

the answer part A) is 

(r,Θ)=(√8,315°)

Part b) (-1, 3)---------> this point belong to the II quadrant

r = √(x² + y²)------ r = √(-1² + (3)²)-----> r=√10

Θ = tan⁻¹ (y/x)---- Θ = tan⁻¹ (3/1)----> 71.57°

remember that the point belong to the II quadrant

so

Θ=180-71.57-----> Θ=108.43°

the answer part B) is 

(r,Θ)=(√10,108.43°)

mark me branlest plz hope it helps

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