SOLUTION: Find all solutions in the interval [0, 2π) {{{ sec^2(x)+6tan(x)=6 }}} Thank you friends

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Question 1101279: Find all solutions in the interval [0, 2π)

Thank you friends
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!


------


tan(x) = -3 + sqrt(14)
tan(x) = -3 - sqrt(14)
etc
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
























Using the + sign:



Approximation:



The tangent is positive in quadrants I and III.

We find the reference angle by using the absolute value,
that is, we find the inverse tangent of +0.7416573868. 
Make sure your calculator is in radian mode:



To get the answer in quadrant I, use the reference
angle.

   <-- that's one solution

To get the answer in quadrant III, add p to the
reference angle.



   <-- that's a second solution

Using the - sign:



Approximation:



The tangent is negative in quadrants II and IV.

We find the reference angle by using the absolute value,
that is, we find the inverse tangent of +6.741657387. 
Make sure your calculator is still in radian mode:



To get the answer in quadrant II, subtract the reference
angle from p



   <-- that's a third solution

To get the answer in quadrant IV, subtract the reference
angle from 2p.



   <-- that's a fourth solution

Edwin
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