The Student Room Group
Reply 1
turtle2
1) If sin(x-a)=cos(x+A), show that tanx=1. (I keep getting tanx=cotx?)

2) Solve sin(x+60)+cos(x+30)=1/2 in the interval 0«x«360. (I got cosx=1 / 2√3 and if i solve from there, it's wrong!)

3) Solve 3tanx=2sinx for 0«x«360.


1)

sinx.cosa-cosx.sina=cosx.cosa-sinx.sina
rearrange
sinx.sina+sinx.cosa=cosx.cosa+cosx.sina
divide by cosx
tanx(sina+cosa)=(cosa+sina)
divide by (cosa+sina)
tanx=1

Aitch
Reply 2
turtle2
1) If sin(x-a)=cos(x+A), show that tanx=1. (I keep getting tanx=cotx?)

2) Solve sin(x+60)+cos(x+30)=1/2 in the interval 0«x«360. (I got cosx=1 / 2√3 and if i solve from there, it's wrong!)

3) Solve 3tanx=2sinx for 0«x«360.


2) I get the same.

First solution: 73.221°
Check LHS:

sin 133.221 + cos 103.221 = 0.5

Aitch
Reply 3
turtle2
1) If sin(x-a)=cos(x+A), show that tanx=1. (I keep getting tanx=cotx?)

2) Solve sin(x+60)+cos(x+30)=1/2 in the interval 0«x«360. (I got cosx=1 / 2√3 and if i solve from there, it's wrong!)

3) Solve 3tanx=2sinx for 0«x«360.


3)3sinx/cosx = 2sinx

sinx = 0
or
3/cosx=2 so
cosx =3/2 discard

so sinx = 0,360? (and 180 - thanks, widowmaker!)

Aitch
Reply 4
Aitch
3)3sinx/cosx = 2sinx

sinx = 0


How do you know this?
Reply 5
Ricki
How do you know this?



Either sinx = 0 or...

so sinx = 0 is a possibility!

Aitch
Reply 6
Aitch
Either sinx = 0 or...

so sinx = 0 is a possibility!

Aitch


I still don't get that. :frown:

I would do this:

3tanx=2sinx
3secx = 2 (by dividing by sinx)
1/cosx = 2/3
x = arccos(3/2), discarded.

:frown: but sinx = 0, is a solution, but I don't get how you get it!!
Reply 7
Ricki
I still don't get that. :frown:

I would do this:

3tanx=2sinx
3secx = 2 (by dividing by sinx)
1/cosx = 2/3
x = arccos(3/2), discarded.

:frown: but sinx = 0, is a solution, but I don't get how you get it!!



When you divide by sinx, you are effectively discarding a solution.

Aitch
Reply 8
Aitch
When you divide by sinx, you are effectively discarding a solution.

Aitch


Oh I see ..

3tanx=2sinx
3sinx/cosx = 2sinx
3sinx/cosx - 2sinx = 0
3sinx - 2sinx = 0, x = 0

:redface:
Reply 9
Ricki
Oh I see ..

3tanx=2sinx
3sinx/cosx = 2sinx
3sinx/cosx - 2sinx = 0
3sinx - 2sinx = 0, x = 0

:redface:


No. The last line is incorrect. After line 3, you can state that

3sinx/cosx - 2sinx = 0 is true if sinx = 0 or if

3/cosx -2 =0

Aitch
--------------
Aitch
No. The last line is incorrect. After line 3, you can state that

3sinx/cosx - 2sinx = 0 is true if sinx = 0 or if

3/cosx -2 =0

Aitch


or Factorise:

3sinx/cosx - 2sinx = 0

sinx ((3/cosx)-2) =0
so
sinx=0
or
(3/cosx)-2=0

Aitch
Ricki
Oh I see ..

3tanx=2sinx
3sinx/cosx = 2sinx
3sinx/cosx - 2sinx = 0
3sinx - 2sinx = 0, x = 0

:redface:


3tanx = 2sinx
3sinx/cosx = 2sinx
3sinx = 2sinxcosx
sinx(3-2cosx) = 0

So sinx = 0 or (3-2cosx) = 0
sinx = 0 OR cosx = 3/2 (discard since out of range)
x = arcsin(0), 180-arcsin(0), arcsin(0)+360
x = 0,180,360o
Reply 11
Widowmaker
sinx(3-2cosx) = 0

x = 0,180,360o


Cheers!! :smile: