t method (1 Viewer)

[kr73114]

can someone explain to me why, when equation has been simplified to a quadratic there is only one answer for theta, while normally there are two.

 

[Rezen]

Could you be more specific or give us an example? A quadratic will have two roots, not necesarrily unique or real.

 

[kr73114]

for example:
3sinx+4cosx=5
using the t method u get:
t=1/3
tanx/2=18.43
tanx=36.86

why is there only one answer and not two?normally you would have tan positive in 3rd quadrant aswell so another answer would be (180+x) but this is not the case when using t method.

 

[Mature Lamb]

Hmm I don't think changing the tan x/2 to tan x means you can double the answer.. unless you get x/2 and x on its own?

 

[ohexploitable]

First off, remember to check 0°, 90°, 180°, 270° and 360°.

tanx/2=18.43
tanx=36.86

Umm...

why is there only one answer and not two?normally you would have tan positive in 3rd quadrant aswell so another answer would be (180+x) but this is not the case when using t method.

If a domain is given the you would find all the solutions within that domain, if a domain isn't given you would just give the solution in general form.

 

[Entrant]

Also, remeber to NEVER square your answer, doing so could introduce extra solutions that were not there before
e.g.

 

[kr73114]

Hmm I don't think changing the tan x/2 to tan x means you can double the answer.. unless you get x/2 and x on its own?

really? well my teacher says so and the answers are right

 

[kr73114]

Also, remeber to NEVER square your answer, doing so could introduce extra solutions that were not there before
e.g.

what would you do then?

 

[ohexploitable]

really? well my teacher says so and the answers are right

Check again...

 

[tommykins]

Brackets people. Use your bloody brackets.

Didn't they teach you this in yr 7?

tanx/2 says NOTHING to us. It could be (tanx)/2 or tan(x/2)

USE THEM.

 

[kr73114]

yeh soz, when i write tanx/2 i mean the tan theta over two things. it is tan(x/2) does that help or am i still misunderstood?

 

[tommykins]

ok if tan(x/2) = 18.43, you can't make tan(x) = 36.86

 

[kr73114]

ok if tan(x/2) = 18.43, you can't make tan(x) = 36.86

ofcourse, that makes sense i made a mistake.

 

[kr73114]

t=1/3
x/2=18.43
x=36.86

yeh i realieze my mistake now i think.
can someone tell me why (180+36.86) isnt an answer?

 

[Trebla]

t=1/3
x/2=18.43
x=36.86

yeh i realieze my mistake now i think.
can someone tell me why (180+36.86) isnt an answer?

It depends on the domain you are given.

If that question said solve 3sin x + 4cos x = 5 for 0º ≤ x ≤ 360º then note that this implies 0º ≤ x/2 ≤ 180º which rules out the 3rd quadrant when solving for tan(x/2) = 1/3

 

[Handmedown]

Also, remeber to NEVER square your answer, doing so could introduce extra solutions that were not there before
e.g.

x=9???

 

[Entrant]

x=9???

yeah sorry, should be that
square root nine equals to plus/minus 3 but it states that x should only be 9. So you shouldn't square it.
Anyway, its off the Cambridge 3U textbook.

 

[Handmedown]

The square root of nine is +3
The square root of minus nine is +3i

Perhaps do you mean this?

 

[kr73114]

It depends on the domain you are given.

If that question said solve 3sin x + 4cos x = 5 for 0º ≤ x ≤ 360º then note that this implies 0º ≤ x/2 ≤ 180º which rules out the 3rd quadrant when solving for tan(x/2) = 1/3

omg thanku