Question (1 Viewer)

[Pace_T]

Find a general solution for tan2x = cot x

is there more than one solution?
I tried it out using factorisation etc and got:

x=n*pi + pi/6 or x = pi*n + 7pi/6

Is what I got right? Also, do I write "or" or "and" (there I wrote "or")

The answer I was provided is x= n*pi/3 + pi/6

Cheers.

 

[who_loves_maths]

Originally Posted by Pace_T
Find a general solution for tan2x = cot x

is there more than one solution?
I tried it out using factorisation etc and got:

x=n*pi + pi/6 or x = pi*n + 7pi/6

Is what I got right? Also, do I write "or" or "and" (there I wrote "or")

The answer I was provided is x= n*pi/3 + pi/6

hi Pace_T,

a 'general solution' implies the existence of many solutions, and in terms of trigonometry, usually depends upon whether or not 'n' is even or odd (but in this particular case, it doesn't matter):

tan(2x) = cot(x) ---> tan(2x) = tan(pi/2 -x) .......................................... (1)

now, you'd know that the general solution of all 'Tan' functions take the form:
If tan(x) = tan(a), then x = n*pi + a , where 'n' is integral.

and applying that to equation (1) , you'd get:

2x = n*pi + (pi/2 -x) ---> 3x = n*pi + pi/2 ---> x = n*pi/3 + pi/6

hence, the general solution is: x = n*pi/3 + pi/6


hope that helps

 

[richz]

hi Pace_T,

a 'general solution' implies the existence of many solutions, and in terms of trigonometry, usually depends upon whether or not 'n' is even or odd (but in this particular case, it doesn't matter):

tan(2x) = cot(x) ---> tan(2x) = tan(pi/2 -x) .......................................... (1)

now, you'd know that the general solution of all 'Tan' functions take the form:
If tan(x) = tan(a), then x = n*pi + a , where 'n' is integral.

and applying that to equation (1) , you'd get:

2x = n*pi + (pi/2 -x) ---> 3x = n*pi + pi/2 ---> x = n*pi/3 + pi/6

hence, the general solution is: x = n*pi/3 + pi/6


hope that helps

how did u get cotx = tan(pi/2-x)?

 

[Pace_T]

its a general rule
like sinx = cos(90-x)
cosx = sin(90-x)

secx= cosec(90-x)
cosecx = sec(90-x)

and then there's cotx = tan(90-x)
tanx = cot(90-x)
i think that's right
ive just heard of these last night !

thanks who_loves_maths!

 

[richz]

o lol i thut he ment (pi)/(2-x) lol opps

 

[currysauce]

ive just heard of these last night !

really, i learnt complementary angles in year 11, like right near the start

 

[Slidey]

I suppose he means he remembered them just last night, after forgetting them completely and utterly last year.