Results 1 to 11 of 11

Math Help - Derivatives/Integrals, properties of sin/cos

  1. #1
    Junior Member
    Joined
    Jul 2008
    Posts
    51

    Derivatives/Integrals, properties of sin/cos

    Q: ʃʃ cos (x +2y) dy dx where 0 < x < pi; 0 < y < pi/2

    When I integrate cos(x+2y) wrt y, do I get sin(x+2y)/2? How do I evaluate sin(x + pi)?

    Does sin (x+c) = sin(x) + sin(c)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by crabchef View Post
    Does sin (x+c) = sin(x) + sin(c)?

    Not, not at all. But \sin(x+\pi)=-\sin(x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2008
    Posts
    51
    Quote Originally Posted by Mathstud28 View Post
    Not, not at all. But \sin(x+\pi)=-\sin(x)
    thanks...but why does sin(x+pi)=-sin(x)?

    also, what does sin(x+c)= ? or are there no general properties associated with that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jul 2008
    From
    Sofia, Bulgaria
    Posts
    75
    Quote Originally Posted by crabchef View Post
    thanks...but why does sin(x+pi)=-sin(x)?

    also, what does sin(x+c)= ? or are there no general properties associated with that?
    1. check with the unit circle ...or

    2. plot the graph of sin(x+pi) , i.e. translation by pi to the left. It comes -sinx out

    3. use trig identities (I don't recommend the last method)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by crabchef View Post
    thanks...but why does sin(x+pi)=-sin(x)?

    also, what does sin(x+c)= ? or are there no general properties associated with that?
    How are you doing double integrals but you don't know the addition formulas for sin?

    \sin\left(A+B\right)=\sin\left(A\right)\cos\left(B  \right)+\cos\left(A\right)\sin\left(B\right)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jul 2008
    Posts
    51
    Quote Originally Posted by Mathstud28 View Post
    How are you doing double integrals but you don't know the addition formulas for sin?

    \sin\left(A+B\right)=\sin\left(A\right)\cos\left(B  \right)+\cos\left(A\right)\sin\left(B\right)
    The last math course I took was 6 years ago...and then I went straight to multi-variate calc without any review.

    Anyway, the formula you gave is if A and B are both variables right? What about in the case that one is a variable and the other is a contant? Do I just treat the constant as a variable and plug it through?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by crabchef View Post
    The last math course I took was 6 years ago...and then I went straight to multi-variate calc without any review.

    Anyway, the formula you gave is if A and B are both variables right? What about in the case that one is a variable and the other is a contant? Do I just treat the constant as a variable and plug it through?
    Yes.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    \int_0^{\pi} \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy~dx

    Ignore the outer integral and do the inner one first.

    \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy

    You can treat x as a constant here. Let u=x+2y. Don't forget to change the integration limits. Then you can plug this in the outer integral and the rest is easy..

    Also you can use the trigonometric addition formula and Fubini's theorem.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641
    Quote Originally Posted by wingless View Post
    \int_0^{\pi} \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy~dx

    Ignore the outer integral and do the inner one first.

    \int_0^{\frac{\pi}{2}}\cos (x+2y)~dy

    You can treat x as a constant here. Let u=x+2y. Don't forget to change the integration limits. Then you can plug this in the outer integral and the rest is easy..

    Also you can use the trigonometric addition formula and Fubini's theorem.
    Would there really be a need for Fubini's Theorem here?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Quote Originally Posted by Mathstud28 View Post
    Would there really be a need for Fubini's Theorem here?
    I would use it to split \int\int \sin (A) \cos (B)~dy~dx to \int \sin(A)~dx ~\int \cos(B)~dy, A being a function of x and B being a function of y. Oh, this is not the theorem itself, but a use of it.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Jul 2008
    Posts
    51
    Quote Originally Posted by Mathstud28 View Post
    How are you doing double integrals but you don't know the addition formulas for sin?

    \sin\left(A+B\right)=\sin\left(A\right)\cos\left(B  \right)+\cos\left(A\right)\sin\left(B\right)
    thank you both for your help. I was wondering if I hate integrated the first part right. I know you recommended substitution to solve it, but it seems like it wouldn't be completely necessary. Thoughts?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Using properties of integrals
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 9th 2010, 06:36 AM
  2. Comparison properties of integrals?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 29th 2010, 06:55 PM
  3. Replies: 5
    Last Post: January 31st 2010, 01:11 PM
  4. Replies: 4
    Last Post: February 10th 2009, 10:54 PM
  5. Properties of Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 13th 2009, 01:26 PM

Search Tags


/mathhelpforum @mathhelpforum