SOLUTION: Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in Quadrant III.

Question 881256: Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in Quadrant III.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of sin (x+y) if sin x = 4/5 in Quadrant II and tan y = 12/5 in Quadrant III.
***
Identity:sin(x+y)=sinx*cosy+cosx*siny
sinx=4/5, (3-4-5 reference right triangle in quadrant II in which sin>0, cos<0.)
cosx=-3/5
..
tany=12/5 (5-12-13 reference right triangle in quadrant III in which sin<0, cos<0.)
siny=-12/13
cosy=-5/13
..
sin(x+y)=4/5*-5/13+-3/5*-12/13=-20/65+36/65=16/65
..
Calculator check:
sinx=4/5 in Q2
x≈126.87˚
tany=12/5 in Q3
y≈247.38˚
x+y ≈374.25˚
sin(x+y)=sin(374.2˚)≈0.2461�
Exact value=16/65≈0.2461�
RELATED QUESTIONS
If sin x= -4/5 and x is in quadrant III, find the value of... (answered by jrfrunner)

If sin x = 4/5 and x is an angle in Quadrant II, find the value of tan... (answered by solver91311)

If sin(x) = −3/5 and x is an angle in Quadrant III, find the value of... (answered by stanbon,lwsshak3)

suppose sin(x) = 3/5 with x in quadrant I, and cos(y) = 12/13 with y in quadrant IV. find (answered by lwsshak3)

if sec x = square root 5/2 with angle x in quadrant IV and tan y= -1/3 with angle y in... (answered by stanbon,Theo)

Find the exact value given that sin A = -4/5 with A in quadrant IV, tan B= 7/24 with B in (answered by stanbon)

find the exact value of cos(a+b) if sin a =4/5 and sin b= -5/13 ( - in 5 only)with a in... (answered by stanbon)

Find the exact value of cos(x-y) if sinx= 4/5 in Quadrant II and tan y=12/5 in Quadrant... (answered by lwsshak3)

Evaluate each expression under the given conditions. tan(x+y) given cos(x)=-(1/3) (answered by richard1234)