Results 1 to 14 of 14
Like Tree4Thanks
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL
  • 1 Post By MarkFL

Math Help - Solving trig equations using identity and proving identites PLEASE help!

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Solving trig equations using identity and proving identites PLEASE help!

    I need some help with the domains of trig equations.
    I have solved all the equations i believe with the right answers, , you can recheck it if you feel comfortable.

    a. cos2x+cosx=0
    ANS:
    2cosx^2+cosx-1
    (2cosx-1)(cosx+1)
    x = 1/2 and x = -1

    x = pi/3 ,5pi/3 and -pi

    are these the right answers in the domain x is an element [-pi,pi) - i believe the [ means equal to and the bracket means doesnt equal

    b. 2cosx^2+3sinx=0
    2(1-sinx^2)+3sinx=0
    2-2sinx^2+3sinx
    2sinx^2-3sinx-2
    (2sinx-1)(sinx+2)
    sinx=1/2 sinx=-2 - cancels since -2 isnt on the unit circle
    x = 30 and 150 degrees -- in the domain [0,360]


    c. cos2x-cosx^2=0
    2cosx^2-1-cosx^2
    cosx^2-1
    (cosx+1)(cosx-1)
    cosx=-1 cosx= 1
    x = pi and 0 ---- in the domain [-pi,pi]


    i just have a hard time with these domains for the trig equations, can someone please check over my answers to see if it fits the domains, or if i have to get rid of some answers or add some answers.

    Thank you in advance




    proving identities.

    cosx-sinx/cosx = 1-tanx

    can someone prove this identity for me?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    1.)

    a) 5pi/3 is not in the given interval. You need to find the equivalent angle that is.

    b) You factored the quadratic in sin(x) incorrectly.

    c) You are missing a solution.

    Identity: assuming you meant to type (cos(x) - sin(x))/cos(x) = 1 - tan(x)

    Use the property of fractions \frac{a-b}{c}=\frac{a}{c}-\frac{b}{c} then use \tan(x)\equiv\frac{\sin(x)}{\cos(x)}.
    Thanks from skg94
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    well thank you for pointing out my errors but can you be more specific?

    i did them to the best of my ability and thank you for the proving identites
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    i figured out my error in b its -2 and +1
    can you please help me with the domain, telling me its just wrong doesnt help me much, sorry if that sounds rude but im having some major difficulty with the - to + domains
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    for a) would it be just pi/3 and pi?
    and for b is it 300 degrees an 210?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    For a), 5pi/3 is a good angle, you just need to subtract 2pi from it to get an equivalent angle in the given interval. Or use cos(-x) = cos(x).

    For b) it would be 210° and 330°. See you want (180+30)° and (360 - 30)°.
    Thanks from skg94
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    oops i made the mistake of thinkin i was a tall triangle for a second

    so it would become -pi/3, pi/3 and negative pi? since i cannot use pi since pi is not included in the domain, or would negtiave pi be negated as well.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    You can use -pi, but not pi since is is not part of the interval.
    Thanks from skg94
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    thank you very much, if you dont mind me asking one more question.

    If <a and <b are both in quadrant 3, sina=-3/5 cosb=-5/13

    find tan(a-b)

    i did tan(5-13)
    (tan5-tan13)/(1+(tan5*tan13)) = (5-13)/(1+(5*13)) = -8/66 = -4/33

    is this correct? it seems off
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    I would use the fact that sine and cosine are both negative in quadrant 3 to state:

    \cos(a)=-\sqrt{1-\sin^2(a)}=-\frac{4}{5}

    \sin(b)=-\sqrt{1-\cos^2(b)}=-\frac{12}{13}

    and so:

    \tan(a-b)=\frac{\sin(a-b)}{\cos(a-b)}=\frac{\sin(a)\cos(b)-\cos(a)\sin(b)}{\cos(a)\cos(b)+\sin(a)\sin(b)}=

    \frac{- \frac{33}{65}}{ \frac{56}{65}}=- \frac{33}{56}
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    hm thats interesting never apporached it like that how come i get a different answer using the formula

    tan(a-b) = tanA-tanB / 1+tanAtanB

    did i substitute the numbers wrong? tan is the hyp if im correct.

    I was under the impression that any and all of these forumlas that are related are supposed to give you the same answer
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    The tangent function is opposite over adjacent.
    Thanks from skg94
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    45

    Re: Solving trig equations using identity and proving identites PLEASE help!

    oh yes... stupid mistake thank you mark you have helped me tons
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Solving trig equations using identity and proving identites PLEASE help!

    Hey, glad to be of assistance!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving Trig. Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 20th 2010, 08:05 PM
  2. help on proving trig identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 22nd 2009, 09:18 AM
  3. Proving/Solving trig equations
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: April 19th 2009, 06:38 PM
  4. proving a trig identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 17th 2009, 02:52 PM
  5. proving trig identity
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: May 19th 2008, 05:49 PM

Search Tags


/mathhelpforum @mathhelpforum