SOLUTION: What is the value of sin(A+B) if {{{ sin A = - (3)/(5) }}} and {{{ cos B= (3)/(5) }}} , and both A and B are in the fourth quadrant?

Algebra ->  Trigonometry-basics -> SOLUTION: What is the value of sin(A+B) if {{{ sin A = - (3)/(5) }}} and {{{ cos B= (3)/(5) }}} , and both A and B are in the fourth quadrant?      Log On


   

Question 955044: What is the value of sin(A+B) if +sin+A+=+-+%283%29%2F%285%29+ and +cos+B=+%283%29%2F%285%29+ , and both A and B are in the fourth quadrant?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29
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sin%28A%29=-3%2F5
sin%5E2%28A%29%2Bcos%5E2%28A%29=1
9%2F25%2Bcos%5E2%28A%29=1
cos%5E2%28A%29=16%2F25
cos%28A%29=4%2F5
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cos%28B%29=3%2F5
sin%5E2%28B%29%2Bcos%5E2%28B%29=1
sin%5E2%28B%29%2B9%2F25=1
sin%5E2%28B%29=16%2F25
sin%28B%29=-4%2F5
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So then,
sin%28A%2BB%29=%28-3%2F5%29%283%2F5%29%2B%284%2F5%29%28-4%2F5%29
sin%28A%2BB%29=-9%2F25-16%2F25
sin%28A%2BB%29=-1