Results 1 to 4 of 4

Math Help - sin(arcsin(x/3)) why just positive?

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    Riverside
    Posts
    9
    Thanks
    2

    sin(arcsin(x/3)) why just positive?

    Which of the following expressions is equal to sin(arccos(x/3))?

    The answer is sqrt(9-x^2)/3. I am wondering why it is not "+ or -" sqrt(9-x^2)/3?

    My rationale is that cos is positive in both the 1st and 4th quadrant so when I take sin of the angle represented by arccos(x/3) I should have to take the sin from both those quadrants.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1781
    Awards
    1

    Re: sin(arcsin(x/3)) why just positive?

    Quote Originally Posted by Jzon758 View Post
    Which of the following expressions is equal to sin(arccos(x/3))?

    The answer is sqrt(9-x^2)/3. I am wondering why it is not "+ or -" sqrt(9-x^2)/3?

    My rationale is that cos is positive in both the 1st and 4th quadrant so when I take sin of the angle represented by arccos(x/3) I should have to take the sin from both those quadrants.
    The range of the arccosine of is [0,\pi] on that domain the sine function is non-negative.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2012
    From
    Riverside
    Posts
    9
    Thanks
    2

    Re: sin(arcsin(x/3)) why just positive?

    I see... is there a way to analytically, without a calculator, determine the range of inverse trig functions?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1781
    Awards
    1

    Re: sin(arcsin(x/3)) why just positive?

    Quote Originally Posted by Jzon758 View Post
    Is there a way to analytically, without a calculator, determine the range of inverse trig functions?
    If I were you, I would just learn the domain and range for each.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Positive eigenvalues implies positive definite
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 16th 2012, 08:16 PM
  2. Positive Sequence with Positive Limit
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 17th 2011, 04:27 PM
  3. Replies: 1
    Last Post: June 9th 2010, 06:23 AM
  4. Proof: positive definite and positive eigenvalues
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 16th 2009, 12:06 PM
  5. Every Positive Number Has A Unique Positive Square Root
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 2nd 2008, 09:26 AM

Search Tags


/mathhelpforum @mathhelpforum