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Math Help - Sum and Difference Identity question

  1. #1
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    Sum and Difference Identity question

    So far i have been able to do all the homework questions that i have for this, except these two.

    Find the exact value for sin(x-y) under the given conditions.

    sinx=24/25,0<x<pie/2; cosy=4/5,0<y<pie/2

    and

    sinx=2/3,pie/2<x<pie; siny=sqrt(7)/4,0<y<pie/2

    Sry for writing out all the "pie's" and sqrt, but i don't know where to find the ascii equivalent.

    Thanks!

    P.S. Can you please explain if you skip steps or something because we just learned this and im trying to follow step by step.
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  2. #2
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    1) There are different ways to do question 1, but if you draw two right angle triangles for the equations you have, its very clear and can help you understand.

    For example  sin\,x = \frac{24}{25} = \frac{opposite}{hypotenuse} -> Construct a right angle triangle and label one of the angles (Angle ABC in the diagram below) x. The opposite side of that angle will be 24 units long, and the hypotenuse is 25 units long.


    From those triangles, you could easily derive the adjacent side via Pythagoras's theorem. (25-24=49 = 7)

    With all the sides, you can now find the exact value of sin x, cos x, sin y, and cos y, using your basic trigonometry ratios.
    Then simply use  sin (x-y) = sin\,x\,cos\,y - cos\,x\,sin\,y

    Do the same for question 2.

    Because we are not considering any obtuse angles (no angle in a right angle triangle can be greater than \frac{\pi}{2}) , all our angles are within your limits.
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