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avatar+472 

θ lies in Quandrant I

 

cos θ = 5/6

 

What is the exact value of sin θ in simplified form?

 

A.  -√11/6

 

B. √11/5

 

C. √11/6

 

D. - 5√11 / 11

 Nov 27, 2018
 #1
avatar+5172 
+1

\(\sin^2(\theta) + \cos^2(\theta)=1\\ \sin^2(\theta) = 1 - \cos^2(\theta) =\\ 1 - \dfrac{25}{36} = \dfrac{11}{36} \\ \text{so }\sin(\theta) = \sqrt{\dfrac{11}{36}} \text{ or }-\sqrt{\dfrac{11}{36}} \\ \text{ and we must use the quadrant info to determine which one} \\ \text{we are told } \theta \text{ lies in quadrant I, thus }\sin(\theta)\geq 0\\ \text{and it must be that }\sin(\theta) = \sqrt{\dfrac{11}{36}}=\dfrac{11}{6}\\ \text{This is choice C} \)

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 Nov 27, 2018
 #2
avatar+101360 
+1

Rom  made  a slight typo

 

√[ 11/36] = √11/√36 = √11 / 6

 

No biggie...!!!

 

 

 

cool cool cool

CPhill  Nov 27, 2018

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