MATH 153E
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. (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.
- (2p.) Find the area of the region that lies inside both curves: r2 = 2sin 2𝜃 , 𝑟 = 1.
- (2p.) Find all points of intersection of the given curves.: r= sin 2𝜃 , 𝑟 = sinϴ.
- (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
