√3 sin 2θ = cos 2θ

Domain: 0o ≤ θ ≤ 360o

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- Jul 16th 2008, 06:09 AMsweetGSolve for θ over the given domain
**√3 sin 2****θ = cos 2θ**

Domain: 0o ≤ θ ≤ 360o - Jul 16th 2008, 08:16 AMSoroban
Hello, sweetG!

Quote:

$\displaystyle \sqrt{3}\sin2\theta \:=\:\cos2\theta\qquad 0^o \leq \theta \leq 360^o$

Then: .$\displaystyle 2\theta\;=\;30^o,\: 210^o,\: 390^o,\: 570^o $

Therefore: .$\displaystyle \theta \;=\;15^o,\:105^o,\:195^o,\:285^o$

- Jul 18th 2008, 07:36 AMsweetG
Thanks so much Soroban that really helped a lot :)

But I've forgotten how to do one thing......how did you get the answers that come after 30 degrees i.e. 210, 390 and 570 degrees. I've forgotten how do these types of questions:( - Jul 18th 2008, 09:11 AMSimplicity
The $\displaystyle \tan \theta$ function has a period of $\displaystyle 180^{\circ}$ hence when you add $\displaystyle 180^{\circ}$, you get the value for $\displaystyle \theta$ which will satisfy your equation. There are infinite solution hence questions usually provide a range (in this case $\displaystyle 0^o \leq \theta \leq 360^o$).

- Jul 19th 2008, 07:07 AMsweetG
Thanks Soroban and Air that really helped and now I'm a lot more clearer on how to do these types of questions :)