Question 936036: Given that tanx=-1/2 and x is in the fourth quadrant, what is the exact value of cosx? Found 3 solutions by stanbon, Alan3354, srinivas.g:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Given that tanx=-1/2 and t is in the fourth quadrant, what is the exact value of cos(t)?
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By definition, tan = y/x
Since tan = -1/2 and the angle is in QIV, y = -1 and x = 2
Then r = sqrt[x^2+y^2] = sqrt[1^2 + 2^2] = sqrt(5)
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Ans: cos = x/r = 1/sqrt(5)
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Cheers,
Stan H.
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You can put this solution on YOUR website! Given that tanx=-1/2 and x is in the fourth quadrant, what is the exact value of cosx?
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tan = y/x = -1/2
Use the terminal point (2,-1)
--> r = sqrt(5)
cos = x/r = 2/sqrt(5)
cos = 2sqrt(5)/5
You can put this solution on YOUR website! Tanx = -1/2
As per Pythagorean Theorem
base^2+ height ^2 = hypotenuse ^2
2^2 +1^2 = hypotenuse ^2
4+1 = hypotenuse ^2
5 = hypotenuse ^2
Sqrt(5) = hypotenus
Cos x = adjacent side / hypotenuse
Cos x = 2/sqrt(5)
IN 4 th quadrant cosx is always positive
Result : Cos x = 2/ sqrt(5)
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