SOLUTION: Suppose sin x= 2/7, sin y= -1/5, cos x= 3 √5/7, cos y= -2 √6/ 5 Find sin(x+y), cos(x+y), tan(x+y)

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose sin x= 2/7, sin y= -1/5, cos x= 3 √5/7, cos y= -2 √6/ 5 Find sin(x+y), cos(x+y), tan(x+y)      Log On


   



Question 1198298: Suppose sin x= 2/7, sin y= -1/5, cos x= 3 √5/7, cos y= -2 √6/ 5
Find sin(x+y), cos(x+y), tan(x+y)

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose sin x= 2/7, sin y= -1/5, cos x= 3 √5/7, cos y= -2 √6/ 5
Find sin(x+y), cos(x+y), tan(x+y)
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Look up "Half-angle formulas" on Wikipedia

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
sin+%28x%29=+2%2F7
sin+%28y%29=+-1%2F5
cos%28x%29=+3sqrt%285%29%2F7
cos+%28y%29=+-2sqrt%286%29%2F5

Find
sin%28x%2By%29=cos%28y%29+sin%28x%29+%2B+cos%28x%29+sin%28y%29
sin%28x%2By%29=%28+-2sqrt%286%29%2F+5%29+%282%2F7%29+%2B+%283sqrt%285%29%2F7%29%28-1%2F5%29
sin%28x%2By%29=-%284sqrt%286%29%29%2F35-%283sqrt%285%29%29%2F35
sin%28x%2By%29=-3%2F%287sqrt%285%29%29+-+%284sqrt%286%29%29%2F35


cos%28x%2By%29=cos%28x%29+cos%28y%29+-+sin%28x%29+sin%28y%29
cos%28x%2By%29=%283sqrt%285%29%2F7%29+%28-2sqrt%286%29%2F+5%29+-+%282%2F7%29+%28-1%2F5%29
cos%28x%2By%29=-%286sqrt%2830%29%29%2F35%2B2%2F35
cos%28x%2By%29=%282%2F35%29+%281+-+3sqrt%2830%29%29


+tan%28x%2By%29=sin%28x+%2B+y%29%2Fcos%28x+%2B+y%29

tan%28x%2By%29=%281%2F538%29+%2875sqrt%285%29+%2B+49sqrt%286%29%29
tan%28x%2By%29=%281%2F538%29+sqrt%283+%2814177+%2B+2450+sqrt%2830%29%29%29

approximately:
sin%28x%2By%29=-0.4716
cos%28x%2By%29=-0.8818
tan%28x%2By%29=-0.4716%2F-0.8818=0.53482