Question 786289: if sin(theta)=5/6, theta in quadrant 2, find the exact value of tan (theta+pi/4
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! if sin(theta)=5/6, theta in quadrant 2, find the exact value of tan (theta+pi/4)
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use x for theta
cosx=√(1-sin^2x)=√(1-25/36)=√(11/36)=√11/6
tan x=sinx/-cosx=-5/√11(In quadrant 2, sin>0, cos<0, and tan<0)
use tan addition formula:
tan(x+π/4)=(tanx+tan(π/4))/(1-tanx*tan(π/4))
tan(π/4)=1
tan(x+(π/4))=(-5/√11)+1/(1-(-5/√11*1)
tan(x+(π/4))=(1-5/√11)/(1+5/√11)
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