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1. Hi, I don't seem to be getting the same answer as the book.

3cot theta=2sin theta

When I work this question out I get theta to equal 1/6th. And thus the value for cos^-1 to be 80.4. But apparently the correct answer is 60. I would really appreciate some help.
2. 3cotx = 2sinx
3cosx/sinx =sinx
(then multiply by sinx)
so 3cosx = 2sin^2x
then use rearranged 2sin^2 +2cos^2 = 2
so 3cosx = 2- 2cos^2x
2cos^2x + 3cosx - 2=0
(2cosx-1)(cosx+2)
so cosx=1/2 and cosx=-2 (but the second one isn't a valid solution)
and if you inverse cosx with the value of 1/2 you get 60 (and 300)
3. (Original post by lizzz111)
3cotx = 2sinx
3cosx/sinx =sinx
(then multiply by sinx)
so 3cosx = 2sin^2x
then use rearranged 2sin^2 +2cos^2 = 2
so 3cosx = 2- 2cos^2x
2cos^2x + 3cosx - 2=0
(2cosx-1)(cosx+2)
so cosx=1/2 and cosx=-2 (but the second one isn't a valid solution)
and if you inverse cosx with the value of 1/2 you get 60 (and 300)
But when you take the inverse of 3 cot x should you also take the inverse of 2sinx. To give 3cos/sin=1/2sin
4. ill use x for theta as its easier to type
3 cot x =2sinx
change cotx to cosx/ sinx
so 3cosx/sinx = 2sinx
times through by sinx
so 3 cosx= 2sin^2x
change sin^2x to 1-cos^2x
so 3cosx=2-2cos^2x
2cos^2x+3cosx-2=0
for cosx= 1/2 and -2
reject -2 as solution
solve cosx=1/2 for x=60

hope this helps
5. (Original post by mathshelp1956)
But when you take the inverse of 3 cot x should you also take the inverse of 2sinx. To give 3cos/sin=1/2sin
yeah mathshelp may have explained the first identity better

its not taking the inverse because
cot = 1/tan
and tan =sin/cos

therefore cot is the same as cos/sin

6. (Original post by Mentalmirz)
ill use x for theta as its easier to type
3 cot x =2sinx
change cotx to cosx/ sinx
so 3cosx/sinx = 2sinx
times through by sinx
so 3 cosx= 2sin^2x
change sin^2x to 1-cos^2x
so 3cosx=2-2cos^2x
2cos^2x+3cosx-2=0
for cosx= 1/2 and -2
reject -2 as solution
solve cosx=1/2 for x=60

hope this helps
Thank you, I was just wondering when you take the inverse of 3 cot x shouldn't you do the same to the other side to give cosx/sinx=1/sinx. Then you multiply both sides by sinx. Thanks
7. (Original post by lizzz111)
yeah mathshelp may have explained the first identity better

its not taking the inverse because
cot = 1/tan
and tan =sin/cos

therefore cot is the same as cos/sin

Right, so If i was doing 1/tan thenI would have to do 1/sin? But because I am doing the inverse twice I don't have to do anything to the sinx, is that right? Thank you
8. (Original post by mathshelp1956)
Right, so If i was doing 1/tan thenI would have to do 1/sin? But because I am doing the inverse twice I don't have to do anything to the sinx, is that right? Thank you
well you are doing 1/tan because cot=1/tan

if you think of the left hand side of the equation, you're not actually changing it
you have 3cotx
and cotx=1/tan
this is using an identity so 1/tan means the same as cot
and then instead of using tan you use the identity tan=sin/cos
so its like 1/(sin/cos) which is cos/sin
so you don't inverse or change the value of the LHS at all so you don't change RHS
so 2sinx stays unchanged

(but yes, if you inversed something twice essentially you haven't changed it so the other side would stay the same)
9. (Original post by mathshelp1956)
Thank you, I was just wondering when you take the inverse of 3 cot x shouldn't you do the same to the other side to give cosx/sinx=1/sinx. Then you multiply both sides by sinx. Thanks
ah okay, you aren't taking the inverse because cotx is equal to cosx/sinx just as tanx is equal to sinx/cosx . It is just an identity so you don't do anything to the rest of the equation.
10. (Original post by lizzz111)
well you are doing 1/tan because cot=1/tan

if you think of the left hand side of the equation, you're not actually changing it
you have 3cotx
and cotx=1/tan
this is using an identity so 1/tan means the same as cot
and then instead of using tan you use the identity tan=sin/cos
so its like 1/(sin/cos) which is cos/sin
so you don't inverse or change the value of the LHS at all so you don't change RHS
so 2sinx stays unchanged

(but yes, if you inversed something twice essentially you haven't changed it so the other side would stay the same)
I understand it now, thank you so much. You're a saint.
11. (Original post by Mentalmirz)
ah okay, you aren't taking the inverse because cotx is equal to cosx/sinx just as tanx is equal to sinx/cosx . It is just an identity so you don't do anything to the rest of the equation.
Thanks very much, I understand it now.
12. (Original post by mathshelp1956)
I understand it now, thank you so much. You're a saint.

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