Given r = 6 cos θ 2 , a. Replace r , θ by r , π − θ in the equation. Does this show that the graph of the equation is symmetric with respect to the line θ = π 2 ? b. The ordered pair − r , 2 π − θ is another representation of the point r , π − θ . Replace r , θ by − r , 2 π − θ in the equation. Does this show that the graph of the equationis symmetric with respect to the line θ = π 2 ? c. What other type of symmetry (if any) does the graph of the equation have? d. Use a graphing utility to graph the equation on a graphing utility for 0 ≤ θ ≤ 4 π .
Given r = 6 cos θ 2 , a. Replace r , θ by r , π − θ in the equation. Does this show that the graph of the equation is symmetric with respect to the line θ = π 2 ? b. The ordered pair − r , 2 π − θ is another representation of the point r , π − θ . Replace r , θ by − r , 2 π − θ in the equation. Does this show that the graph of the equationis symmetric with respect to the line θ = π 2 ? c. What other type of symmetry (if any) does the graph of the equation have? d. Use a graphing utility to graph the equation on a graphing utility for 0 ≤ θ ≤ 4 π .
Solution Summary: The author analyzes the graph of the polar equation r=6mathrmcostheta 2.
a. Replace
r
,
θ
by
r
,
π
−
θ
in the equation. Does this show that the graph of the equation is symmetric with respect to the line
θ
=
π
2
?
b. The ordered pair
−
r
,
2
π
−
θ
is another representation of the point
r
,
π
−
θ
. Replace
r
,
θ
by
−
r
,
2
π
−
θ
in the equation. Does this show that the graph of the equationis symmetric with respect to the line
θ
=
π
2
?
c. What other type of symmetry (if any) does the graph of the equation have?
d. Use a graphing utility to graph the equation on a graphing utility for
0
≤
θ
≤
4
π
.
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