Results 1 to 3 of 3

Math Help - Cos and Sin Question

  1. #1
    Junior Member
    Joined
    May 2008
    From
    California
    Posts
    36

    Cos and Sin Question

    If cos−1(a)=0 and sin−1(6)=b, then the exact value of sin(a+b) is
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    arccos(a) = 0
    So, a = cos(0) = 1
    And pi(a) = pi(1) = pi
    So,
    sin[pi(a)] = sin(pi) = 0
    cos[pi(a)] = cos(pi) = -1

    arcsin(pi/6) = b
    So, pi/6 = sin(b)
    And, cos(b) = sqrt[1 -sin^2(b)] = sqrt[1 -(pi/6)^2]

    sin(pi(a) +b)
    = sin(a*pi)cos(b) +cos(a*pi)sin(b)
    = (0)(sqrt[1 -(pi/6)^2] +(-1)(pi/6)
    = -pi/6 ---------------------answer.
    Last edited by ticbol; October 9th 2008 at 04:59 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member mrmohamed's Avatar
    Joined
    Dec 2009
    From
    Egypt
    Posts
    43

    Lightbulb

    Quote Originally Posted by ticbol View Post
    arccos(a) = 0
    So, a = cos(0) = 1
    And pi(a) = pi(1) = pi
    So,
    sin[pi(a)] = sin(pi) = 0
    cos[pi(a)] = cos(pi) = -1

    arcsin(pi/6) = b
    So, pi/6 = sin(b)
    And, cos(b) = sqrt[1 -sin^2(b)] = sqrt[1 -(pi/6)^2]

    sin(pi(a) +b)
    = sin(a*pi)cos(b) +cos(a*pi)sin(b)
    = (0)(sqrt[1 -(pi/6)^2] +(-1)(pi/6)
    = -pi/6 ---------------------answer.
    Hi all
    just small question
    what is pi here in the red line??
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum