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Math Help - Can you please help me with this quick question?

  1. #1
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    Can you please help me with this quick question?

    α and β are acute angles in quadrant I, with sin α = 7/25 and cos B = 5/13. Determine the value of sin (α + β)

    The answer is 323 / 325

    I started with
    sin (α + β) = sin α cos β + cos α sin β
    α = 7/25
    B = 5/13
    sin (7/25) cos (5/13) + cos (7/25) sin (5/13)

    Is that even right? If so, where do you go from there?
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  2. #2
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    I started with
    sin (α + β) = sin α cos β + cos α sin β
    α = 7/25 no
    B = 5/13 no
    sin (7/25) cos (5/13) + cos (7/25) sin (5/13) and no
    you were given values for sin a and cos b ... sketch reference triangles in quad I for each angle, then determine cos a and sin b


    sin a = 7/25 ... cos a = 24/25

    cos b = 5/13 ... sin b = 12/13

    sin(a+b) = sin a cos b + cos a sin b

    sin(a+b) = (7/25)(5/13) + (24/25)(12/13)
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  3. #3
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    Oh, ok. I get it now. Thanks
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  4. #4
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    Quote Originally Posted by lanvin View Post
    α and β are acute angles in quadrant I, with sin α = 7/25 and cos B = 5/13. Determine the value of sin (α + β)

    The answer is 323 / 325

    I started with
    sin (α + β) = sin α cos β + cos α sin β
    α = 7/25
    B = 5/13
    sin (7/25) cos (5/13) + cos (7/25) sin (5/13)

    Is that even right? If so, where do you go from there?
    You're on the right track. Another way is to remember

    \cos^2{x} + \sin^2{x} = 1.

    You can use this to find \cos{\alpha} and \sin{\beta}.
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