Trigonometric Functions And Identities

[wanchosen]

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 can't factor this or solve for x. Can anyone help please?

 

[Hurkyl]

Can anyone help please?

Why did you spend all of that effort to turn it into a quadratic equation?

 

[wanchosen]

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.

 

[Hurkyl]

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?

 

[wanchosen]

Completing the square, or using the quadratic formula are another two methods.

 

[wanchosen]

Thanks, tried completing the square to solve the quadratic and this worked.