SOLUTION: 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

Click here to see ALL problems on Trigonometry-basics

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)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
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)
***
sin a=-4/5 (-π/4 < a < 0 )(Q4)
cos a=3/5 (working with a (3-4-5) reference right triangle in quadrant IV)
a≈306.87˚
..
cos b=-5/13(π/2 < b < π )(Q2)
sin b=12/13(working with a (5-12-13) reference right triangle in quadrant II)
b≈112.62˚
..
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≈306.87˚-112.62˚≈194.25˚
sin(a-b)≈sin(194.25≈-0.2462
Exact value=-16/65≈-0.2462

SOLUTION: 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)