Results 1 to 5 of 5

Math Help - Find the exact value of s in the given interval that has the given function value

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    San Diego
    Posts
    37
    Thanks
    3

    Find the exact value of s in the given interval that has the given function value

    a) [pi, 3pi/2 ] ; sin(s) = -(sqrt of 2)/2

    b) [pi/2, pi] ; csc(s) = 2

    c) [3pi/2, 2pi] ; cos(s) = (sqrt of 3)/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,324
    Thanks
    1241

    Re: Find the exact value of s in the given interval that has the given function value

    Quote Originally Posted by boltage619 View Post
    a) [pi, 3pi/2 ] ; sin(s) = -(sqrt of 2)/2

    b) [pi/2, pi] ; csc(s) = 2

    c) [3pi/2, 2pi] ; cos(s) = (sqrt of 3)/2
    The focus angle will be the angle in the first quadrant, so

    \displaystyle \begin{align*} \sin{(\theta)} &= \frac{\sqrt{2}}{2} \\ \theta &= \frac{\pi}{4} \end{align*}.

    We know that the sine value is negative in the third and fourth quadrants, and from the domain given, we know the angle needs to be in the third quadrant.

    So the angle is \displaystyle \begin{align*} \pi + \frac{\pi}{4} = \frac{5\pi}{4} \end{align*}.


    Can you do something similar for the other two questions?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    San Diego
    Posts
    37
    Thanks
    3

    Re: Find the exact value of s in the given interval that has the given function value

    Well the square root of 2/2 is actually negative, not positive.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,324
    Thanks
    1241

    Re: Find the exact value of s in the given interval that has the given function value

    You obviously didn't read what I posted. You need to work out the FOCUS angle first, which is in the first quadrant, where the sine values (and all other values) are positive. Then once you have the focus angle you add/subtract it to whatever you need to so that you end up in the correct quadrant. In this case, since you need to sweep out a full semicircle to go from the first quadrant to the third, you need to add an angle of \displaystyle \begin{align*} \pi \end{align*} to your focus angle.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2013
    From
    San Diego
    Posts
    37
    Thanks
    3

    Re: Find the exact value of s in the given interval that has the given function value

    Alright, thanks for explaining that to me!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 22nd 2010, 05:24 PM
  2. Finding exact solutions in the interval
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 30th 2010, 12:05 AM
  3. Find Exact solution over the interval [0.2pi)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 13th 2009, 10:07 AM
  4. Replies: 8
    Last Post: May 3rd 2009, 03:26 PM
  5. Find interval of function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 08:09 PM

Search Tags


/mathhelpforum @mathhelpforum