Solving Trigonometric Equations

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Solving Trigonometric Equations

Mathematics
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post the equation when you are ready :)
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write in terms of just cos by using Pythagorean identity

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Other answers:

whats that?
you will have a quadratic equation in terms of cos(theta)
\[\sin^2(\theta)+\cos^2(\theta)=1 \text{ is one of the pythagorean identities }\]
\[\sin^2(\theta)=1-\cos^2(\theta)\]
\[3(1-\cos^2(\theta))=1+\cos(\theta) \\ 3-3\cos^2(\theta)=1+\cos(\theta)\]
if you want replace cos(theta) with u for now \[3-3u^2=1+u\] solve for u
by first putting everything on one side
but i have a range to follow
and i got u=1
hmmm how did you get u=1?
\[3-3u^2=1+u \\ \text{ add } 3u^2 \text{ and subtract } 3 \text{ on both sides } \\ 0=3u^2+u+1-3 \\ 0=3u^2+u-2 \\ 0=(3u-2)(u+1)\]
neither u+1=0 or 3u-2=0 leads to u=1
but anyways you have the following equations to solve recall we replaced cos(theta) with u so we actually have \[\cos(\theta)+1=0 \text{ or } 3\cos(\theta)-2=0 \] you need to solve these two equations for theta

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