SOLUTION: if sec(theta)=5/3 and theta lies in quadrant i, find sin(theta+pi/6)

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Question 933577: if sec(theta)=5/3 and theta lies in quadrant i, find sin(theta+pi/6)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if sec(theta)=5/3 and theta lies in quadrant i, find sin(theta+pi/6)
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if sec(theta)=5/3 --> cos(t) = 3/5
cos^2 + sin^2 = 1 --> sin(t) = 4/5
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sin(t + pi/6) = sin(t)cos(pi/6) + sin(pi/6)cos(t)
= (4/5)*sqrt(3)/2 + (1/2)*(3/5)
= 4sqrt(3)/10 + 3/10