Question 921702
given sin alpha=-4/5, -pi/4 is less than alpha is less than 0; cos beta= -5/13, pi/2 is less than beta is less than pi, find sin (alpha - beta)
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sin a=-4/5 (-&#960;/4 < a < 0 )(Q4)
cos a=3/5 (working with a (3-4-5) reference right triangle in quadrant IV)
a&#8776;306.87&#730;
..
cos b=-5/13(&#960;/2 < b < &#960; )(Q2)
sin b=12/13(working with a (5-12-13) reference right triangle in quadrant II)
b&#8776;112.62&#730;
..
Identity: sin(a-b)=(sin a*cos b)-(cos a*sin b)=(-4/5*-5/13)-(3/5*12/13)=20/65-36/65=-16/65
calculator check:
a-b&#8776;306.87&#730;-112.62&#730;&#8776;194.25&#730;
sin(a-b)&#8776;sin(194.25&#8776;-0.2462
Exact value=-16/65&#8776;-0.2462