anonymous
  • anonymous
Question Part Points Submissions Used Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) tan2(x) = 3 2 sec(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\tan^2(x)= (3/2)\sec(x)\] here is the equation better
jim_thompson5910
  • jim_thompson5910
\[\large \tan^2(x)= \frac{3}{2}\sec(x)\] \[\large \sec^2(x)-1= \frac{3}{2}\sec(x)\] \[\large z^2-1= \frac{3}{2}z\] \[\large 2(z^2-1)= 3z\] \[\large 2z^2-2= 3z\] \[\large 2z^2-2-3z = 0\] \[\large 2z^2-3z-2 = 0\] Now use the quadratic formula to solve for z. Tell me what you get.
anonymous
  • anonymous
ok sec

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anonymous
  • anonymous
I get z = -(1/2), 2
jim_thompson5910
  • jim_thompson5910
so this means that sec(x) = -1/2 or sec(x) = 2 because z = sec(x)
jim_thompson5910
  • jim_thompson5910
solve each equation for x
jim_thompson5910
  • jim_thompson5910
one of those equations has no solutions at all
anonymous
  • anonymous
I'm confused on the next step
jim_thompson5910
  • jim_thompson5910
sec(x) = -1/2 1/cos(x) = -1/2 cos(x) = -2 what's next?
anonymous
  • anonymous
1/cos(2)
anonymous
  • anonymous
im guessing im wrong
jim_thompson5910
  • jim_thompson5910
use the unit circle and tell me when cos(x) = -2 is true
anonymous
  • anonymous
it doesn't exist right?
jim_thompson5910
  • jim_thompson5910
good, there are no solutions
jim_thompson5910
  • jim_thompson5910
sec(x) = 2 1/cos(x) = 2 cos(x) = 1/2 what are the solutions here?
anonymous
  • anonymous
pi/3 , 5pi/3 ?
jim_thompson5910
  • jim_thompson5910
good, those are your two solutions
anonymous
  • anonymous
yay... thank you soo much!
jim_thompson5910
  • jim_thompson5910
you're welcome

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