Results 1 to 3 of 3

Math Help - Sin Cos Tan...

  1. #1
    Newbie
    Joined
    Oct 2005
    Posts
    2

    Post Sin Cos Tan...

    I thought I knew how to work out these equations, but my answer was different from the answer they gave.

    Given: a and B are first-quadrant angles, sin a = 5/13 and cos B = 3/5, evaluate cos (a+B).

    I used the equations sin^2 a + cos^2 a = 1 to get cos a = 12/13. That would make cos (a+B) 99/65. However, their answer was 16/65. Help, please? Another one:

    Given: a and B are first-quadrant angles, sin a = 5/13 and cos B = 3/5, evaluate sin (a-B).

    I used the same equations to get sin B = 4/5, and thus sin (a-B) = -27/65. Their answer was -33/65. Please help me out!!!

    ~Cassie
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    You got wrong answers because you thought
    cos(a+B) = cos(a) +cosB, and sin(a-B) = sin(a) -sinB.

    No.
    The correct expansions are:
    cos(a+B) = cos(a)*cosB -sin(a)*sinB.
    And, sin(a-B) = sin(a)*cosB -cos(a)*sinB

    So, get all the sines and cosines of angles "a" and B, then solve your questions again. You will get them this time.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2005
    Posts
    2
    Ah, I reworked them and got it! Thanks so much!!!!
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum