Hi

cos(θ) = 1/3  Then  sin(θ)= √2/3  Note: 1^2 + (√2)^2 = 3

sin(θ + π/3) = sinθcos(π/3) + cosθsin(π/3)

sin(θ + π/3) = (√2/3)cos(π/3) + (1/3)sin(π/3)

Plug and Play

sin(θ + π/3) = (√2/3)(1/2) + (1/3)(√3/2)  

............

θ	radians	sin θ	cos θ	tan θ

0°	0	0	1	0

30°	π/6	1/2	√3/2	√3/3

45°	π/4	√2/2	√2/2	1

60°	π/3	√3/2	1/2	√3

90°	π/2	1	0	─

      

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
 if cos theta = 1/3, theta is in Q IV, find the exact value of sin(theta+pie/3)

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By definition, cos = x/r

So x = 1 and r = 3

Then y = -sqrt(3^2-1^2] = -sqrt(8)

Therefore 

sin(t) = -sqrt(8)/3 = -(2/3)sqrt(2) 

and cos(t) = 1/3

------------------------------

Ans:: sin(t + pi/3) = sin(t)cos(pi/3)+cos(t)sin(pi/3)

= -(2/3)sqrt(2)*(1/2) + (1/3)(sqrt(3)/2)

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= -sqrt(2)/3 + sqrt(3)/6

----

= [sqrt(3) - 2sqrt(2)]/6

==================

Cheers,

Stan H.

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