Question

GIVING MEDAL N FAN
determine if the graph is symmetric about the x-axis, the y-axis or the orgiin
r= 5 cos 5theta

y-axis only
x-axis, y-axis
x-axis, y-axis, origin
x-axis only

Answer 1

@Michele_Laino

Answer 2

do you know what the graph of cos x looks like?

Answer 3

NO

Answer 4

if f(x) = f(-x) then its symetrical about the y-axis

Answer 5

using the De Moivre formula (complex numbers), we get this identity:
\[\large \cos \left( {5\theta } \right) = {\left( {\cos \theta } \right)^5} - 10{\left( {\cos \theta } \right)^3}{\left( {\sin \theta } \right)^2} + 5\left( {\cos \theta } \right){\left( {\sin \theta } \right)^4}\]

Answer 6

y axis only @Michele_Laino ?

Answer 7

so, we can rewrite your equation as follows:
\[\large r = \left\{ {5{{\left( {\cos \theta } \right)}^5} - 10{{\left( {\cos \theta } \right)}^3}{{\left( {\sin \theta } \right)}^2} + 5\left( {\cos \theta } \right){{\left( {\sin \theta } \right)}^4}} \right\}\]

Answer 8

and going to the cartesian coordinates, we can write:
\[\Large r = \left\{ {5\frac{{{x^5}}}{{{r^5}}} - 10\frac{{{x^3}{y^2}}}{{{r^5}}} + 5\frac{{x{y^4}}}{{{r^5}}}} \right\}\]
so what can you conclude?

Answer 9

is it all 3? x-axis, y-axis, origin

Answer 10

oops... I have made a typo, here is the right equation:
\[\Large r = 5\left\{ {\frac{{{x^5}}}{{{r^5}}} - 10\frac{{{x^3}{y^2}}}{{{r^5}}} + 5\frac{{x{y^4}}}{{{r^5}}}} \right\}\]
we have a symmetry for a variable whose exponent is an even number

Answer 11

omg im lost is it x-axis or y-axis, could u just tell me ? @Michele_Laino

Answer 12

check if f(-60) = f(60) if so then its symmetrical over the y-axis

Answer 13

I think x-axis, since we have this:
\[\Large f\left( {x, - y} \right) = f\left( {x,y} \right)\]

Answer 14

so x-axis everyone @Michele_Laino @welshfella @Astrophysics ??

Answer 15

no i think its y-axis

Answer 16

both??

Answer 17

or just y axis?

Answer 18

just y-axis

Answer 19

ok

Answer 20

because its an even function and graph of cos x is