Question

verify that the polar coordinates (-4, pi/2) satisfies
the equation r=4sin3theta

and sketch a graph of the equation r=4sin3theta and locate the
point from above and approximate the location of any vertical
tangent lines

Answer #1

sketch the curve with the given polar equation by first
sketching the graph of r as a function of theta in Cartesian
coordinates.
r= 1 + 3Sin(theta)

Sketch the curve with the given polar equation by first
sketching the graph of r as a function of θ in Cartesian
coordinates.
r=3sin2θ
and
r= cos3θ
and
r= 4cos(2θ)
Please show symmetry tests
Thank you in advance!

Sketch the graph of the polar equation r = 3 + 2 sin
theta

a) Sketch the graph of r = 1 + sin2θ in polar coordinates with
proper explanation.
b) Find the area of the region that is inside of the cardioid r
= 2+2sinθ and outside of the circle r = 3. Also ﬁnd the area that
is outside of the cardioid and inside of the circle. Hence, ﬁnd the
total area enclosed by these two curves.

given the polar curve r = 2(1+cos theta) find the Cartesian
coordinates (x,y) of the point of the curve when theta = pi/2 and
find the slope of the tangent line to this polar curve at theta =
pi/2

The Cartesian coordinates of a point are given. (a) (−4, 4) (i)
Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤
θ < 2π. (r, θ) (ii) Find polar coordinates (r, θ) of the point,
where r < 0 and 0 ≤ θ < 2π. (r, θ) (b) (3, 3 3 ) (i) Find
polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ
< 2π. (r, θ) =...

1. Sketch the polar function r = (θ − π/4)(θ − 3π/4) on the
interval 0 ≤ θ ≤ 2π. Then find all lines tangent to this polar
function at the point (0, 0).
2. Find the area of the region enclosed by one loop of the curve
r = 5 sin(4θ).
3. Use the Monotone Sequence Theorem to determine that the
following sequence converges: an = 1/ 2n+3 .

1) Point R has cylindrical coordinates (5, pi/6, 4). Plot R and
describe its location in space using rectangular or cartesian
coordinates.
Please explain and show your steps.
2) Describe the surface with cylindrical equation r =6.
Please explain and show your steps. Thank you

1) Sketch the graph?=? ,?=? +3,and include orientation.
2) Sketch the graph ? = sin ? , ? = sin2 ? + 3 and include
orientation.
3) Remove the parameter for ? = ? − 3, ? = ?2 + 3? − 2 and write
the corresponding
rectangular equation.
4) Remove the parameter for ? = 2 + 3 sin ? , ? = −1 + 3 cos ?
and write the corresponding rectangular equation.
5) Create a parameterization for...

If r = 1 + sin(3θ) is the equation of a polar graph, find the
slope of the tangent line when θ = π

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