Results 1 to 4 of 4

Thread: Finding all of the angles when sec(3x)

  1. #1
    Member
    Joined
    Mar 2011
    Posts
    99

    Thumbs up Finding all of the angles when sec(3x)

    Hi Forum
    I have some ideas myself on this one, but I'd love to hear how you guys would proceed in this scenario.

    Find the sum of all solutions in the interval $\displaystyle [0,2\pi)$ for the equation $\displaystyle sec(3x)=\sqrt2$

    First, we can put this in the form $\displaystyle cos(3x)=\frac{1}{\sqrt2}$ for better viewing.
    We know that $\displaystyle cos(x)=\frac{1}{\sqrt2}$ is $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{7\pi}{4}$.

    Then our period will equal $\displaystyle \frac{2\pi}{3}$, so the distance from one $\displaystyle \sqrt2$ to another is $\displaystyle \frac{\pi}{3}$
    Since our $\displaystyle \sqrt2$ will appear 3 times faster because of the $\displaystyle 3x$, our first $\displaystyle \sqrt2$ is $\displaystyle \frac{\pi}{12}$

    Now, can we just go summing it to $\displaystyle \frac{\pi}{3}$ until we get to $\displaystyle 2\pi$?
    What do you guys think?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9

    Re: Finding all of the angles when sec(3x)

    Quote Originally Posted by Zellator View Post
    Hi Forum
    I have some ideas myself on this one, but I'd love to hear how you guys would proceed in this scenario.

    Find the sum of all solutions in the interval $\displaystyle [0,2\pi)$ for the equation $\displaystyle sec(3x)=\sqrt2$

    First, we can put this in the form $\displaystyle cos(3x)=\frac{1}{\sqrt2}$ for better viewing.
    We know that $\displaystyle cos(x)=\frac{1}{\sqrt2}$ is $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{7\pi}{4}$.

    Then our period will equal $\displaystyle \frac{2\pi}{3}$, so the distance from one $\displaystyle \sqrt2$ to another is $\displaystyle \frac{\pi}{3}$
    Since our $\displaystyle \sqrt2$ will appear 3 times faster because of the $\displaystyle 3x$, our first $\displaystyle \sqrt2$ is $\displaystyle \frac{\pi}{12}$

    Now, can we just go summing it to $\displaystyle \frac{\pi}{3}$ until we get to $\displaystyle 2\pi$?
    What do you guys think?

    Thanks!
    I think you should find all the values of x that lie in the given interval and then add them up.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,237
    Thanks
    33

    Re: Finding all of the angles when sec(3x)

    Hi Zellator, you have the right idea

    Quote Originally Posted by Zellator View Post

    First, we can put this in the form $\displaystyle cos(3x)=\frac{1}{\sqrt2}$ for better viewing.
    We know that $\displaystyle cos(x)=\frac{1}{\sqrt2}$ is $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{7\pi}{4}$.
    $\displaystyle \cos(3x)=\frac{1}{\sqrt2}\implies 3x = \frac{\pi}{4},\frac{7\pi}{4}\implies x = \frac{\pi}{12},\frac{7\pi}{12}$

    Now add $\displaystyle \frac{2\pi}{3}$ to these solutions, up to $\displaystyle 2\pi$

    After that add them up as suggested in post #2.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2011
    Posts
    99

    Re: Finding all of the angles when sec(3x)

    Hey mr fantastic and pickslides!

    It's great to know that I am on the right track, then.
    Thanks for your second opinions, that was really appreciated
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. finding angles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 2nd 2011, 07:26 PM
  2. Finding angles in a triangle.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: Feb 5th 2010, 04:30 AM
  3. Finding angles
    Posted in the Trigonometry Forum
    Replies: 20
    Last Post: Jan 15th 2010, 03:37 AM
  4. Finding the measure of angles
    Posted in the Geometry Forum
    Replies: 11
    Last Post: Sep 19th 2007, 07:01 PM
  5. Finding the angles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 4th 2007, 03:43 AM

Search Tags


/mathhelpforum @mathhelpforum