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Math Help - [SOLVED] Given sin A and sin B, find without using a calculator.

  1. #1
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    [SOLVED] Given sin A and sin B, find without using a calculator.

    Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

    cos (A + B)

    Here is my take on the question.

    cos (A + B)
    = cosAcosB - sinAsinB
    = (4/5)cosB - sinA(5/13)

    After this, I don't know how to continue. Answer is 33/65
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  2. #2
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    Presumably you do know that cos^2(A)+ sin^2(A)= 1 and cos^2(B)+ sin^2(B)= 1. Since you know sin(B) and cos(A) (and know that the angles are acute) you can solve for cos(B) and sin(A).
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  3. #3
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    Quote Originally Posted by mark1950 View Post
    Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

    cos (A + B)

    Here is my take on the question.

    cos (A + B)
    = cosAcosB - sinAsinB
    = (4/5)cosB - sinA(5/13)

    After this, I don't know how to continue. Answer is 33/65
    \cos^2 A + \sin^2 A = 1. You know the value of \cos A and you know that A is in the first quadrant. So get the value of \sin A ....

    \cos^2 B + \sin^2 B = 1. You know the value of \sin B and you know that B is in the first quadrant. So get the value of \cos B ....
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  4. #4
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    Quote Originally Posted by mark1950 View Post
    Given that A and B are acute angles with cos A = 4/5 and sin B = 5/13, find without using tables or a calculator

    cos (A + B)

    Here is my take on the question.

    cos (A + B)
    = cosAcosB - sinAsinB
    = (4/5)cosB - sinA(5/13)

    After this, I don't know how to continue. Answer is 33/65
    HI

    good start . You are told that both angles are acute ie <90 which means they are both in the first quadrant .

    Draw a triangle .. with sides 3 , 4 , 5

    sin A = 3/5

    Same goes to the other one . cos B=12/13

    Then put them together .
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  5. #5
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    Thanks, guys! Finally found the answer.
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