SOLUTION: <pre> Given: {{{cos(A)=-7/25}}}, {{{pi < A < 3pi/2}}} {{{sin(B)=-3/5}}}, {{{3pi/2 <B<2pi}}} Find: {{{sin(A-B)}}} {{{tan(A-B)}}}

Given: ,  

       , 



Find: 

       

Answer by Edwin McCravy(20060)   (Show Source): 

You can put this solution on YOUR website!
 
Given: ,  
       , 

Find: 
      

, . That's Q3 

Draw the picture of angle A in the third quadrant Q3. 
Since the cosine is adjacent/hypotenuse or x/r, and since we are given 
, make x=-7 and r=, and calculate y using the 
Pythagorean theorem:

    x²+y² = r²
 (-7)²+y² = 25²
    49+y² = 625
       y² = 576
        y = ±√576
        y = ±24, we take y = -24 

We take y negative because it goes down from the x-axis, 
and we ALWAYS take r positive because it begins on the
right side of the x-axis and doesn't change its sign when
it swings around into the other quadrants. 








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, . That's Q4 
 

Draw the picture of angle B in the fourth quadrant Q4. Since the sine is
opposite/hypotenuse or y/r, and since we are given  ,
make y=-3 and r=5, and calculate x using the Pythagorean theorem:

    x²+y² = r²
 x²+(-3)² = 5²
     x²+9 = 25
       x² = 25
        y = ±√25
        y = ±5, we take y = -5 

We take y negative because it goes down from the x-axis, 
and we ALWAYS take r positive because it begins on the
right side of the x-axis and doesn't change its sign when
it swings around into the other quadrants. 



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Edwin