prelim question (1 Viewer)

[elliottjohnson]

hey,

this is a question concerning the trig topic in the prelim course.
is there a simpler way to do it rather than polynomials since we havent done that part of the course yet.

3tan^3 x - 2tan^2 x - tanx + 1 = 0 solve between 0 and 360 degrees.

thanks

 

[Timothy.Siu]

hey,

this is a question concerning the trig topic in the prelim course.
is there a simpler way to do it rather than polynomials since we havent done that part of the course yet.

3tan^3 x - 2tan^2 x - tanx + 1 = 0 solve between 0 and 360 degrees.

thanks

i dont even know how to do it knowing polynomials lol

 

[EvoRevolution]

+1 yea same i dont think it is possible, or it mite be but i dont know

 

[clintmyster]

have no idea but let tan x = t or something and use all that sum of roots crap till you get something xD or use the cubic formula which is not in our syllabuses.

 

[elliottjohnson]

have no idea but let tan x = t or something and use all that sum of roots crap till you get something xD or use the cubic formula which is not in our syllabuses.

really well its in my fitz textbook.ill ask my teacher. thanks anyway.

 

[addikaye03]

x=327 degress 8' ( nearest min)

Only real root

 

[Timothy.Siu]

wouldn't that be the same as that angle-180?

 

[elliottjohnson]

haha, the Q is acturaly

3tan^3 x - 3tan^2 x - tanx + 1 = 0 solve between 0 and 360 degrees.

the -2tan^2 x changed to -3tan^2 x

sorry , ive got the right answer now anyway.

 

[addikaye03]

haha, the Q is acturaly

3tan^3 x - 3tan^2 x - tanx + 1 = 0 solve between 0 and 360 degrees.

the -2tan^2 x changed to -3tan^2 x

sorry , ive got the right answer now anyway.

Let P(x)=3tan^3 x - 3tan^2 x - tanx + 1

So use the common factors of the constant term to find factors ie. 1=1x1 or -1x-1

So when we try P(1) we get 0 .'. (x-1) is a factor of P(x)

_____________________
Use long division: (x-1) ) (3x^3-3x^2-x+1) Where x=tanx

So in the form P(x)=Q(x)A(x)+R(x) =(x-1)(3x^2-1)

NOW, set this factorisation=0 ( from original part of Q)

(x-1)(3x^2-1)=0

x=1 or/ x^2=1/3

x=1 and x=+-1/rt3 ( plus or minus)

I didn't do type out the long division, hopefully you get what i got, that line is supposed to be the long division line thing

 

[gurmies]

 

[addikaye03]

yer i know i saw that also but i thought i'll show the process which is required for most Q rather than this particular Q, nevertheless good work young Gurmies!

To gurmies: Avoiding msn today are we? lol

 

[jchoi]

Those method above are like all polynomials innit? Anyways, I don't think so, (@ original question) except if you can be bothered, try doing double and triple angles, then putting them all over common denominator.

I think though, it would end up giving only a part of the answer.