solving trig equations

[xc630]

Hi I am having difficulty solving these problems. I would appreciate any help.

The problem says solve for 0</= theta < 360

2 tan squared theta = 3 tan theta -1

I got the equation to

1) tan squared theta - 3 tan theta = -1/2

2) tan theta (tan theta -3) = -1/2

tan theta = -1/2
tan theta = 2.5

Is this correct so far?

 

[Guest]

\(\displaystyle 2tan^2X = 3tanX -1\)

Am I correct in saying this is what you're trying to say (sorry I replaced the theta with X because I don't know how to write theta in LaTex :lol: )

Anyhow, I'd proceed like this:

\(\displaystyle 2tan^2X -3tanX +1 =0\)

Then I'd say \(\displaystyle tanX =u\)
So:
\(\displaystyle 2u^2 -3u +1 =0\)
Then solve the quadratic, I think you were going along the right line but at one point I think you divided by 2 thoughout and missed a term:

tan squared theta - 3 tan theta = -1/2

 

[xc630]

Thanks a lot. I got it down to tan x = SQRT2/2 and tan x= 1

From there I got 35.3, 215.3, 45, and 225 degrees

 

[Guest]

Did you remember to take +(sqrt2)/2 and -(sqrt2)/2?

 

[xc630]

Scratch the 1st two answers. It should be tan x= 1/2

then 26.6 and 206.6 degrees

 

[Guest]

Top stuff, as long as you solved it for yourself, well done dude :lol: