SOLUTION: Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6. find sin(a+b) and cos(a+b). What quadrant is a+b in? Find sin (a-b) and cos(a-b). What quadrant is a-b in?

Algebra ->  Trigonometry-basics -> SOLUTION: Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6. find sin(a+b) and cos(a+b). What quadrant is a+b in? Find sin (a-b) and cos(a-b). What quadrant is a-b in?       Log On


   

Question 943297: Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6.
find sin(a+b) and cos(a+b). What quadrant is a+b in?
Find sin (a-b) and cos(a-b). What quadrant is a-b in?
(If you can help me with the sin and cos of a+b, I can probably figure the others out on my own).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6.
find sin(a+b) and cos(a+b). What quadrant is a+b in?
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sina=2/5
cosa=-√(1-sin^2(a))=-√(1-4/25)=-√(21/25)=-√21/5
sinb=1/2
cosb=√3/2
sin(a+b)=sina*cosb+cosa*sinb=2/5*√3/2+-√21/5*1/2=2√3/10-√21/10=(2√3-√21)/10
cos(a+b)=cosa*cosb-sina*sinb=-√21/5*√3/2-2/5*1/2=-√63/10-2/10=-(√63+2)/10
Check:w/calculator
sina=2/5
a=156.42˚
b=30˚
a+b=186.42 (Quadrant II)
sin(a+b)=sin(186.42)≈-0.1118..
exact value=(2√3-√21)/10≈-0.1118..
..
cos(a+b)=cos(186.42)≈-0.9937..
exact value=-(√63+2)/10≈-0.9937..