Question 730878: { Find the values of sine and cosine function for each angle measure : 2x, given tanx=2 an cosx >0}
Can you explain how to solve this? Also how do I know in what quadrant the cosine and tan are in?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! { Find the values of sine and cosine function for each angle measure : 2x, given tanx=2 an cosx >0}
Can you explain how to solve this? Also how do I know in what quadrant the cosine and tan are in?
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tan>0 in quadrants I and III
cos>0 in quadrants I and IV
Therefore, only in quadrant I are both tan and cos>0
..
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
tan x=O/A=2
O=2, A=1
H=√(A^2+O^2)=√(1+4)=√5
tan x=2
Identity: tan 2x=2tanx/1+tan^2x
=4/(1+4)
=4/5
tan 2x=O/A=4/5
O=4, A=5
H=√(O^2+A^2)=√(16+25)=√41
..
sin 2x=O/H=4/√41
cos 2x=A/H=5/√41
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