Results 1 to 5 of 5

Math Help - what is inverse sine of sin3 equal to?

  1. #1
    Member
    Joined
    Dec 2008
    From
    Australia
    Posts
    161

    what is inverse sine of sin3 equal to?

    Hi,

     \sin^{-1}(sin3) . Find the exact value.

    what is that equal to in exact value?

    it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2.

    I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2010
    From
    Mumbai
    Posts
    91
    Thanks
    2
    acctually in general in the equation <br /> <br />
\sin^{-1}(sin3)<br />
    both the sin's will give no effect because finding sin3 and inversing it again with sin give 3 itself
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    1

    exact answer

    Let the expression be equal to x, x being angle.
    <br />
sin^-1(sin(3))=x<br />
    <br />
sin(x)=sin(3)<br />
    <br />
x=3<br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,691
    Thanks
    449
    Quote Originally Posted by differentiate View Post
    Hi,

     \sin^{-1}(sin3) . Find the exact value.

    what is that equal to in exact value?

    it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2. ... correct

    I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

    Thanks
    note that an angle of measure 3 radians is in quad II.

    \sin(3) = \sin(\pi-3) , where \pi-3 is a quad I angle

    \arcsin[\sin(\pi-3)] = \pi-3
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Quote Originally Posted by baqijan View Post
    Let the expression be equal to x, x being angle.
    <br />
sin^-1(sin(3))=x<br />
    <br />
sin(x)=sin(3)<br />
    <br />
x=3<br />
    Go back and read the original post. 3 is not between -\pi/2 and \pi/2 sin^{-1}(sin(x))= x is only true for x in that range.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: February 20th 2011, 08:24 AM
  2. sine inverse and theta value
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 21st 2010, 08:04 AM
  3. Some inverse and law of sine problems
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 24th 2009, 06:02 PM
  4. need help differentiating cos^(4)3t sin3 tdt
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 15th 2009, 10:56 AM
  5. sine inverse
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 10th 2007, 03:51 AM

Search Tags


/mathhelpforum @mathhelpforum