Trignometric inequations (1 Viewer)

[clever angel]

hi ,

i can't figure out how to solve these questions:

8cosx-6sinx=1.5 in the range 0<x<2pi

ans: 0.777rad,4.219rad

3cos2x-2sin2x=1
ans 0.351,2.203,3.492,5.344rad

help plzzzzzzzzzzz

 

[Estel]

auxiliary method/t-sub...
i'm presuming you have learnt them?

 

[FinalFantasy]

8cosx-6sinx=1.5
16cosx-12sinx=3
(16cosx)^2=(12sinx+3)^2
256cos^2x=144sin^2x+72sinx+9
256-256sin^2x=144sin^2x+72sinx+9
400sin^2x+72sinx-247=0
den use quadratic formula lol

 

[Raginsheep]

Dun u create extra solutions when you square it though? Im not sure... I just heard my teacher saying that or somthing...

 

[FinalFantasy]

but aren't u given the range?
if u are then it doesn't matter

 

[Raginsheep]

Ay....true

 

[FinalFantasy]

3cos2x-2sin2x=1
3cos2x=1+2sin2x
(3cos2x)^2=(1+2sin2x)^2
9cos^2(2x)=1+4sin2x+4sin^2(2x)
9(1-sin^2(2x))=.....
9-9sin^2(2x)=1+4sin2x+4sin^2(2x)
13sin^2(2x)+4sin2x-8=0
hmm.. i dunno.. quadratic from here or something?

 

[mojako]

failure of the quadratic... Fields medal

by inspection,

 

[FinalFantasy]

if not use those quads. den chuck in some t's
sin x=2t\(1+t^2) and cos x=(1-t^2)\(1+t^2)
sure that would do

 

[mojako]

if not use those quads. den chuck in some t's
sin x=2t\(1+t^2) and cos x=(1-t^2)\(1+t^2)
sure that would do

or u can do some sort of inspection

from the quad formula u have
sin(x)=0.700948797 OR -0.880948797
for 0 < x < 2pi, x = 0.7767, 2.3649, 4.219, 5.2053
(assuming there is no human error)

you want 16cosx=3+12sinx

just substitute the four x values using this machine called calculator and see if it satisfies 16cosx=3+12sinx

 

[Xayma]

Dun u create extra solutions when you square it though? Im not sure... I just heard my teacher saying that or somthing...

Yes it will give extra solutions that is why you check them, which you should be doing anyway.

 

[mojako]

oh by the way, how does this belong to "Trignometric inequations"

 

[elizabethy]

hi ,

i can't figure out how to solve these questions:

8cosx-6sinx=1.5 in the range 0<x<2pi

ans: 0.777rad,4.219rad

3cos2x-2sin2x=1
ans 0.351,2.203,3.492,5.344rad

help plzzzzzzzzzzz

hey by now ur a champ when it cumz to solving these...isn't it??
c, u shud always trust ur self!

 

[Kutay]

hmm i did by t-method i got theta = 44 degrees 30 minutes and 241 degrees 45 minutes

 

[Trev]

lol this is such an old thread.
i cant remember how to do t method, i always use transformation

 

[FinalFantasy]

the "t method" is sin x=2t\(1+t²) and cos x=(1-t²)\(1+t²) where t=tan (x\2)

 

[Kutay]

transformation ??? its that like the auxiliary method>>??

 

[Trev]

erm, ive never heard of the term auxiliary method in relation to maths; im talking about
asinx + bcosx = rsin(x + alpha)
where r = (a^2 + b^2)^1/2 and alpha = b/a
is this also referred to as the 'auxiliary' method?

 

[Trev]

the "t method" is sin x=2t\(1+t²) and cos x=(1-t²)\(1+t²) where t=tan (x\2)

i remember what sin,cos,tan is;
you forgot tan;
tanx = 2t/(1-t²)
i just forget hw to use them haha, o well

 

[Slidey]

erm, ive never heard of the term auxiliary method in relation to maths; im talking about
asinx + bcosx = rsin(x + alpha)
where r = (a^2 + b^2)^1/2 and alpha = b/a
is this also referred to as the 'auxiliary' method?

No, that would be the main method used to solve them. It is called transformation.

'Auxiliary' in this case means back-up - the t-method is used as back-up because it is an algebra bash and hence a pain.