## QUIZ 7

MATH quiz代考 Plot each point with the given polar coordinates. Then find two other pairs of polar coordinates of this point, one with r>0 and one with…

### Quiz 7 (Take home Quiz) (Total 15p.) Show your work!  MATH quiz代考

1. 1. (1p.) Plot each point with the given polar coordinates. Then find two other pairs of polar coordinates of this point, one with r>0 and one with r<0:

a) (2,5π/6);                                     b) (3, -π/3).

2.(1p.) Polar coordinates of a point are given. Find the rectangular coordinates of each point.

a) (-1,-π/6);                                    b) (4, 4π/3)

3.1p.) The rectangular coordinates of a point are given. Find polar coordinates of each point

(i) where r > 0 and 0 ≤ ϴ <2π and (ii) where r < 0 and 0 ≤ ϴ <2π. MATH quiz代考

a) (-4,4);                                        b) (-6,0).

4.(1p.) Convert each rectangular equation to a polar equation that expresses r in terms of ϴ:

a) x2 – y2 = 4;                               b) y = x.

5.(1p.)Convert each polar equation to a rectangular equation:

a) ϴ = π/3;                                    b) r2 sin 2𝜃 = 1.

6.(2p.) Test for symmetry and then graph each polar equation (use the grid for polar coordinates):

a) r = 2(1+cos 𝜃);                          b) r2 = 9sin 2𝜃.

#### 7.(2p.) Find the points on the given curve where the tangent line is horizontal or vertical. MATH quiz代考

r = 1 + cos 𝜃.

1. (2p.) Find the area of the region that lies inside both curves: r2 = 2sin 2𝜃 , 𝑟 = 1.
2. (2p.) Find all points of intersection of the given curves.: r= sin 2𝜃 , 𝑟 = sinϴ.
3. (2p.) Find the exact length of the polar curve: r = 2(1+cos 𝜃).Prof. Siranush Bezirganyan, Ph.D. • Winter 2021 • MATH 153E • QUIZ 7 Page 3 of 3

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