SOLUTION: what is the exact value of each expression? a) tan x =3, find tan (x + pi/4) b) sin x = 4/5, x is in quadrant 1, find sin (x + pi/6)

Question 920727: what is the exact value of each expression?
a) tan x =3, find tan (x + pi/4)
b) sin x = 4/5, x is in quadrant 1, find sin (x + pi/6)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the exact value of each expression?
a) tan x =3, find tan (x + pi/4)
Identity: tan(x+y)=(tanx+tany)/(1-tanx*tany)
tan(x+π/4)=tanx+tan(π/4)/(1-tanx*tan(π/4))=(3+1)/(1-3)=4/-2=-2
..
b) sin x = 4/5, x is in quadrant 1, find sin (x + pi/6)
(Working with a 3-4-5 reference right triangle in quadrant I)
cos x=3/5
Identity: sin(x+y)=sinx*cosy+cosx*siny
sin(x+y)=(4/5*cos(π/6)+3/5*sin(π/6)=4/5*√3/2+3/5*1/2=(4√3/10)+(3/10)=(4√3+3)/10
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