Results 1 to 9 of 9

Math Help - When does sin(x)/cos(x) equal 1

  1. #1
    Newbie
    Joined
    Jul 2012
    From
    Brisbane
    Posts
    2

    When does sin(x)/cos(x) equal 1

    I have an equation where solutions to cos(x)=sin(x) are needed. I have been told that sin(x)/cos(x) is equal to tan(x) but also that sin(x)/cos(x)=1. For which value will sin(x)/cos(x) result in 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: When does sin(x)/cos(x) equal 1

    Whenever tan x = 1. For which x is tan x = 1?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2012
    From
    Brisbane
    Posts
    2

    Re: When does sin(x)/cos(x) equal 1

    tan^-1(1)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2012
    From
    Delhi
    Posts
    8
    Thanks
    2

    Re: When does sin(x)/cos(x) equal 1

    sin^2x+cos^2x=1
    if sinx= cosx
    2 sin^2x=1
    sinx= 1/SQRT2
    x=45 Deg
    Last edited by hemvanezi; July 16th 2012 at 03:28 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,492
    Thanks
    1391

    Re: When does sin(x)/cos(x) equal 1

    I believe you'll find that adding all integer multiples of 180 degrees will also work.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: When does sin(x)/cos(x) equal 1

    Another way to do it: On the unit circle, cos x corresponds to the x-coordinate and sin x corresponds to the y-coordinate. Therefore, \sin x = \cos x if and only if the point on the unit circle is such that the x-coordinate equals the y-coordinate, or the point lies on the line y=x. Where does the unit circle intersect the line y=x?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,541
    Thanks
    1394

    Re: When does sin(x)/cos(x) equal 1

    Of course, \frac{sin(x)}{cos(x)}= 1 is the same as sin(x)= cos(x). Since, in basic terms, "sine" and "cosine" refer to opposite angles in a right triangle, if they are equal those angles must be the same- and since those those angles must add to 90 degrees, it should be easy to see what the angle must be. In more advanced terms, where the angles are not in a right triangle, we can use the "circle" formulation and see that adding 180 degrees will also be an angle.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,100
    Thanks
    67

    Re: When does sin(x)/cos(x) equal 1

    Quote Originally Posted by Prove It View Post
    I believe you'll find that adding all integer multiples of 180 degrees will also work.
    D'you mean SIN(x)/COS(90-x) where 90 > x > 0 ?
    Don't "follow" your "180".
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,065
    Thanks
    296

    Re: When does sin(x)/cos(x) equal 1

    Quote Originally Posted by Wilmer View Post
    Don't "follow" your "180".
    ProveIt was pointing out to the previous poster that not only is 45 degrees a solution to sin(x)/cos(x) = 1, but so too are 45 degrees plus or minus n x 180 degrees for n = any integer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equal power sets -> Equal sets?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: July 5th 2012, 09:23 AM
  2. [SOLVED] Is it really equal? Why?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 7th 2010, 11:51 AM
  3. Why is -ln8 equal ln1/8?
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: January 12th 2010, 04:45 AM
  4. what does p+q equal?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 24th 2009, 01:44 PM
  5. Replies: 2
    Last Post: March 23rd 2009, 07:11 AM

Search Tags


/mathhelpforum @mathhelpforum