Trigonometric Functions And Identities

  • Thread starter wanchosen
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  • #1
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Main Question or Discussion Point

Hi there,

I am struggling to solve for x in the following problem:-

Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2

I have used the identity tan^2(x) + 1 = sec^2(x) to get:

sec^2(x) - 1 = 5sec(x) - 2

and rearranged to get

sec^2(x) - 5sec(x) + 1 = 0

but I cant factor this or solve for x. Can anyone help please?
 

Answers and Replies

  • #2
Hurkyl
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Can anyone help please?
Why did you spend all of that effort to turn it into a quadratic equation?
 
  • #3
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I assumed that I need to get all the trig functions of the same type before I can solve for x. Using the identity for sec^2(x) seemed the obvious choice...which lead me to a quadratic. I couldn't see how else to solve for x. I also tried converting everything in terms of cos (x) which was more messy. I may be mistaken, but from previous questions I have answered like this, tend to lead to a quadratic to factor for a solution/s for x.
 
  • #4
Hurkyl
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tend to lead to a quadratic to factor for a solution/s for x.
Is factoring the only method you know for solving quadratic equations, or do you know other methods?
 
  • #5
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Completing the square, or using the quadratic formula are another two methods.
 
  • #6
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Thanks, tried completing the square to solve the quadratic and this worked.
 

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