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    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.
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    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
    rearrange to form a quadratic
    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)
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    (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
    rearrange to form a quadratic
    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
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    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
    slove quadratic
    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
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    (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

    hope this was more helpful
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    (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
    slove quadratic
    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
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    (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

    hope this was more helpful
    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
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    (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)
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    (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.
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    (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.
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    (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.
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    (Original post by mathshelp1956)
    I understand it now, thank you so much. You're a saint.
    glad you get it
 
 
 
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