Results 1 to 4 of 4

Math Help - trig problem: circular functions of real numbers

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    4

    trig problem: circular functions of real numbers

    please help me! I don't understand these problems at all...

    Solve the equation for 0 (less than or equal to) x (less than or equal to) 2pi.

    1. sin x = sin (x+2)
    2. cos x = cos (x+1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by lolo View Post
    please help me! I don't understand these problems at all...

    Solve the equation for 0 (less than or equal to) x (less than or equal to) 2pi.

    1. sin x = sin (x+2)
    2. cos x = cos (x+1)
    sinX = sin(X +2)

    Normally, it would be X = X +2.
    But that leads to nowhere.
    So do it by expansion:

    sinX = sinXcos(2) +cosXsin(2)
    sinX -sinXcos(2) = cosXsin(2)
    sinX(1 -cos(2)) = cosXsin(2)
    Divide both sides by cosX,
    tanX(1 -cos(2)) = sin(2)
    tanX = sin(2) / (1 -cos(2))
    Using the calculator,
    tanX = 0.642096 -------------positive tan, so X is in the 1st or 3rd quadrants.

    X = arctan(0.642096) = 0.570796 radian

    In the 1st quadrant,
    X = 0.570796 radian -----------answer.

    In the 3rd quadrant,
    X = pi +0.570796 = 3.712389 radians ---------answer.

    ------------------------------------
    You should be able to solve the second equation now.

    You should find that X is in the 2nd or 4th quadrants,
    and X = 2.641593 or 5.783185 radians.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    4
    Quote Originally Posted by ticbol View Post
    sinX = sin(X +2)

    Normally, it would be X = X +2.
    But that leads to nowhere.
    So do it by expansion:

    sinX = sinXcos(2) +cosXsin(2)
    sinX -sinXcos(2) = cosXsin(2)
    sinX(1 -cos(2)) = cosXsin(2)
    Divide both sides by cosX,
    tanX(1 -cos(2)) = sin(2)
    tanX = sin(2) / (1 -cos(2))
    Using the calculator,
    tanX = 0.642096 -------------positive tan, so X is in the 1st or 3rd quadrants.

    X = arctan(0.642096) = 0.570796 radian

    In the 1st quadrant,
    X = 0.570796 radian -----------answer.

    In the 3rd quadrant,
    X = pi +0.570796 = 3.712389 radians ---------answer.

    ------------------------------------
    You should be able to solve the second equation now.

    You should find that X is in the 2nd or 4th quadrants,
    and X = 2.641593 or 5.783185 radians.
    thanks for replying! I found out it's the right answer, but I don't understand where the cos came from when you expanded sin(x+2), can you explain it please?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by lolo View Post
    thanks for replying! I found out it's the right answer, but I don't understand where the cos came from when you expanded sin(x+2), can you explain it please?
    You mean the following?
    sin(X +1) = sinXcos1 +cosXsin1 ?

    You thought that should have been
    sin(X +1) = sinX +sin1 ?

    The first one is the correct one. That is how it is done with trig functions.

    -----------------
    Example: Find sin(30deg +60deg).

    The correct way:
    sin(30deg +60deg)
    = sin(30deg)cos(60deg) +cos(30deg)sin(60deg)
    = (1/2)(1/2) +(sqrt(3)/2)(sqrt(3)/2)
    = 1/4 +3/4
    = 1

    A wrong way:
    sin(30deg +60deg)
    = sin(30deg) +sin(60deg)
    = 1/2 +sqrt(3)/2
    = [1 +sqrt(3)] / 2

    Well, of course, sin(30deg +60deg) = sin(90deg) = 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Circular Functions & Trig
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 15th 2010, 12:40 AM
  2. Trigonometric Functions of Real Numbers
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: January 31st 2010, 11:32 AM
  3. Unit Circle: Trig Functions of Real Numbers
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: December 1st 2009, 06:18 PM
  4. Circular Functions Problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 5th 2009, 04:01 AM
  5. Trig Identities and finding real numbers
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 4th 2009, 06:06 AM

Search Tags


/mathhelpforum @mathhelpforum