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 2 years ago
2sin^4(z) + 7cos(z) = 4, between 0 and 360 inclusive.
i could turn sin^4(z) into 1cos^4(z), and then turn that into (1+cos^2(z))(1cos^2(z)), but then what??
 2 years ago
2sin^4(z) + 7cos(z) = 4, between 0 and 360 inclusive. i could turn sin^4(z) into 1cos^4(z), and then turn that into (1+cos^2(z))(1cos^2(z)), but then what??

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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3how is sin^4(z) = 1cos^4(z) ??

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2then what can i do here??

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3maybe (1cos^2 x)^2 = (1 2 cos^2 x + cos^4 x) (i have used sin^2 + cos^2= 1, so sin^2 = 1cos^2)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.324y^2+2y^4+7y=4.......by putting y=cos x not easy to solve, can u use calculator?

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0Where is the question from?

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1cos z= (1+ sin 2z)/2 and let's say sin z= y ..you are done

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3trignometry only, i guess

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3how would that help @jasonxx ? what about sin 2x then?

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1it'll be a quadratic equation and it is done

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1something like 2y^2.....

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3quadratic?? u have sin2x not sin^2 x

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1wait a sec guys ..we all are confused the question is

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[2 \sin^4 z+ 7 \cos z=4\]

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[\cos z= \sqrt {1 \sin^2 z}\] let's say \[\sin^2 z= y\] now i think it can be done

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3u just increased the complexity by bringing square root sign....

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[2y^2+7(\sqrt{1y})=4\] \[2y^24=7 \sqrt{1y}\] square both sides and then let's say y^2=z

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1yea ..there could be alternative

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3so u will get the same equation with y^4 which i hace posted

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[4y^48y^2+16=49(1y)\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3even that is not any simpler to solve

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@tanvidais13 stuck or done lol, because you seem to be frozen ;)

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2sorry, guests over, had to "entertain" :P

Coolsector
 2 years ago
Best ResponseYou've already chosen the best response.0are you sure you wrote the question correctly ?

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1no it is done wait a sec

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sin^4 z= (\sin^2z)^2= (1\cos^2z)^2\] now \[12\cos^2z+\cos^4z=(1\cos^2z)^2\]

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2what jasonxx wrote in the beginning is right.

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@tanvidais13 hope i entertained lol

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3didn't entertain, didn't solve.... and the last thing u did,was the 1st thing i did

Coolsector
 2 years ago
Best ResponseYou've already chosen the best response.0you are writing the same thing again

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2wait i STILL didn't get how you got 1−2cos^2(z)+cos^4(z)=(1−cos^2(z))2 what is that???

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@hartnn i know you might be fillipn out..relax mate, try to see things from everyone's visual angel

Coolsector
 2 years ago
Best ResponseYou've already chosen the best response.0(ab)^2 = a^2 2ab + b^2

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2oh yeahh, so that was just the expansion.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(sin^2 x+cos^2 x =1\)and that expansion

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@tanvidais13 i wrote sin^2 z = 1 cos^ z and that was an expansion

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[(1 \cos^2 z)= \sin^2 z\] and \[(1\cos^2z)^2= expansion (ab)^2\] ;)

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2but then we only get cosz in powers of 1,2, and 4, not three. can we still solve it like that??

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1yes you can...with a basic rearrangement

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[\cos^4z2\cos^2z+1+7cosz=4\] now can you play with this equation , see something is common among them, which can be shotned

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1\[2 \cos^4z4\cos^2z+2+7\cos z =4\]

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.2@jasonxx I request you to please don't interrupt when some one is helping a user. No worries, if you were ONLY giving suggestion but if you are spoiling the work of the previous user then it will not be nice.

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.2Do refer : http://openstudy.com/codeofconduct

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@mathslover i do respect your words but i can't stop myself from some arrogant person and his haughty comment i am sure you know, whom am i talking about

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2if we say cos(z) = y, then we will have \[2y^4  4y^2 + 7y  2 = 0\]

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@tanvidais13 \[2y^44y^2=27y\] now? can you do the rest

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.2@jasonxx please stay friendly dude. It would be better if you have not used "arrogant" like words, this makes the whole difference. It's nice to see that you respect my words but I will say that even I am spoiling this post now, so I am leaving , you may continue your help but remember the following things from now onwards: i) Never give direct answer to any asker. ii) Don't give direct solution to the asker, this not only ends the motive of openstudy but also not helps asker. iii) Let the asker do the work, you must suggest him/her regarding your idea or steps. like : 5x7=3 , just say "Try to add 7 both sides, what do you get?" iv) "Answer snipping" , this is what you have likely done here, if a user is helping the asker then please don't interrupt by giving direct solution or any way, but if you have good ideas then just post shortly. Thanks :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3see my 4th comment, 35 minutes ago, we are back there, we wasted 35 minutes..

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@mathslover thank you but you should not be biased..well for the sake of us i am putting this to an end, i haven't copied i was friendly and i was working the way i believe is dood and is in accordance with this code of conduct but if one is willing to have my welcome in some other way then i am sorry, either i'll help or i shall feel compelled to assault someone verbally ...my serious apology for being rude thank you

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.2Thanks and sorry if i was rude, but now someone help @tanvidais13 :)

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@Mikael have a look, i believe you can take us outta this

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@tanvidais13 if we take value of Z=0 degrees ... this equation fails !! are you sure this question is correct?

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.12*0+7*1 can't be equal to 4 ?? isn't it?

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1@mathslover what say bro? :) any idea !!

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.2@sauravshakya and @UnkleRhaukus

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1doesn't it look like equation that is not consistent ..it fails whilst substituting the value of z

Coolsector
 2 years ago
Best ResponseYou've already chosen the best response.0but you had to find z .. you dont plug any value you want

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1good point, but how one is supposed to get value of somethin from (not sure) an incorrect equation

Coolsector
 2 years ago
Best ResponseYou've already chosen the best response.0who said that it is incorrect

jasonxx
 2 years ago
Best ResponseYou've already chosen the best response.1intuition ...let me solve this again :)

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0Cant this be factored:dw:1348921637348:dw

siddhantsharan
 2 years ago
Best ResponseYou've already chosen the best response.0We have to find roots?Or do we have to find number of roots?

siddhantsharan
 2 years ago
Best ResponseYou've already chosen the best response.0The question doesnt specify. I dont think you can find the exact root to this. http://www.wolframalpha.com/input/?i=2x%5E4++4x%5E2+%2B+7x++2

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3http://www.wolframalpha.com/input/?i=24y%5E2%2B2y%5E4%2B7y%3D4 y=0.35 can be cos z, other two are imaginary and last is 2 cos z cannot be 2 so cos z=0.35

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3but unfortunately, we cannot use a calculator here....

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0So, it has only two real solutions.

siddhantsharan
 2 years ago
Best ResponseYou've already chosen the best response.0Precisely. And the other real root (not 2) is Probably not possible to compute by pen and paper.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1348922391902:dw AND I was trying to prove it has no real solution as the above equation is never 0 for 1<=t<=1..... But I was doing all wrong.

tanvidais13
 2 years ago
Best ResponseYou've already chosen the best response.2so the only possible answer is cos(z) = 0.35, only the problem is it's basically impossible to find out by hand :P anyways, THANK YOU SO MUCH, everyone, for this strangeretricehellofaproblem :P AND this includes all the relative latecomers :P I can't give a medal to everyone, but I wish I could :P

estudier
 2 years ago
Best ResponseYou've already chosen the best response.0If you absolutely have to find it by hand and you can make an initial guess which is close enough, then you could perhaps use Newton's method to get the root.
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