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anonymous
 one year ago
GIVING MEDAL N FAN
determine if the graph is symmetric about the xaxis, the yaxis or the orgiin
r= 5 cos 5theta
yaxis only
xaxis, yaxis
xaxis, yaxis, origin
xaxis only
anonymous
 one year ago
GIVING MEDAL N FAN determine if the graph is symmetric about the xaxis, the yaxis or the orgiin r= 5 cos 5theta yaxis only xaxis, yaxis xaxis, yaxis, origin xaxis only

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.1do you know what the graph of cos x looks like?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1if f(x) = f(x) then its symetrical about the yaxis

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2using the De Moivre formula (complex numbers), we get this identity: \[\large \cos \left( {5\theta } \right) = {\left( {\cos \theta } \right)^5}  10{\left( {\cos \theta } \right)^3}{\left( {\sin \theta } \right)^2} + 5\left( {\cos \theta } \right){\left( {\sin \theta } \right)^4}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y axis only @Michele_Laino ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2so, we can rewrite your equation as follows: \[\large r = \left\{ {5{{\left( {\cos \theta } \right)}^5}  10{{\left( {\cos \theta } \right)}^3}{{\left( {\sin \theta } \right)}^2} + 5\left( {\cos \theta } \right){{\left( {\sin \theta } \right)}^4}} \right\}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2and 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it all 3? xaxis, yaxis, origin

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2oops... 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0omg im lost is it xaxis or yaxis, could u just tell me ? @Michele_Laino

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1check if f(60) = f(60) if so then its symmetrical over the yaxis

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2I think xaxis, since we have this: \[\Large f\left( {x,  y} \right) = f\left( {x,y} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so xaxis everyone @Michele_Laino @welshfella @Astrophysics ??

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1no i think its yaxis

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1because its an even function and graph of cos x is dw:1438441043404:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2if it is yaxis, then we shoul have this: \[\Large f\left( {  x,y} \right) = f\left( {x,y} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2nevertheless x compares with odd exponent

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1and that is the case , i think

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2\[f\left( {  x,y} \right) = 5\left\{ {\frac{{  {x^5}}}{{{r^5}}}  10\frac{{  {x^3}{y^2}}}{{{r^5}}} + 5\frac{{  x{y^4}}}{{{r^5}}}} \right\} =  f\left( {x,y} \right)\] am I right?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.1would like to discuss firther but got to go

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2I think taht we have both symmetries with respect to xaxis and the origin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Guys can we solve this by using thisdw:1438442042055:dw now for eq r=5cos5theta .the equation will be symmetric about Y axis if r is unchanged for theta =180theta.. and symmetric about x axis if r is unchanged for theta =360theta.Since the first one is not true from from basic trigonometric relation of cos(180theta)=costheta.Hence above equation is symmetric only about X axis for which equality still holds...Just a thought..Dont know what the direction change (negative or positive) actually means though..Oen for thoughts..
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