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Solve the equation in (0, 2pi) using any appropriate method. Answer in radians rounded to four decimal places.

\(\frac{1-sin^2x}{cot^2 x} =\frac{\sqrt{3}}{3}\)

 

a. 0.8631, 2.2785, 4.0047, 5.4201 

b. 0.6888, 2.4528, 3.8304, 5.5944

c. 0.8631, 0.7077, 2.4339, 2.2785

d. 0.6888, 08820, 2.4339, 2.4528

Guest Sep 6, 2017
 #1
avatar+86859 
+1

 [ 1 - sin^2 (x) ] / cot^2 (x)  =

 

[ cos ^2 (x) ] /  [ cos^2 (x) / sin^2(x) ]

 

sin^2 (x) =   sqrt (3)  / 3         take both roots

 

sin (x)  =   ± sqrt ( 1/ √ 3) 

 

So.....      arcsin (  sqrt ( 1/ √ 3)  )  ≈  0.8631       and    pi - 0.8631 ≈  2.2785

 

And   arcsin ( -  sqrt ( 1/ √ 3)  )  ≈   5.4201    and   pi + 0.8631  ≈  4.0047

 

The first answer is correct

 

 

cool cool cool

CPhill  Sep 6, 2017

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