anonymous
  • anonymous
Solving Trigonometric Equations
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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freckles
  • freckles
post the equation when you are ready :)
anonymous
  • anonymous
|dw:1436825812888:dw|
freckles
  • freckles
write in terms of just cos by using Pythagorean identity

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