Here’s a trig precalc question I’m stuck on!

[jrami103]

The question says if cos2theta=1/3 and it’s within the domain 0 to 2pi, what would costheta be equal to. I got the answer down to be radical 6 over 3 however I’m not sure if it it’s plus or minus or only positive. Thanks! (it’s number 7 down below)

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[MarkFL]

Hello, and welcome to FMH!

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[Dr.Peterson]

The question says if cos2theta=1/3 and it’s within the domain 0 to 2pi, what would costheta be equal to. I got the answer down to be radical 6 over 3 however I’m not sure if it it’s plus or minus or only positive. Thanks! (it’s number 7 down below)

If [MATH]\cos(2\theta) = 1/3[/MATH], and [MATH]0\le\theta\lt 2\pi[/MATH], then [MATH]0\le 2\theta\lt 4\pi[/MATH]. What quadrants might [MATH]2\theta[/MATH] be in? What quadrants might [MATH]\theta[/MATH] be in?