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anonymous
 one year ago
Solving Trigonometric Equations
anonymous
 one year ago
Solving Trigonometric Equations

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freckles
 one year ago
Best ResponseYou've already chosen the best response.0post the equation when you are ready :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436825812888:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.0write in terms of just cos by using Pythagorean identity

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you will have a quadratic equation in terms of cos(theta)

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin^2(\theta)+\cos^2(\theta)=1 \text{ is one of the pythagorean identities }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[\sin^2(\theta)=1\cos^2(\theta)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[3(1\cos^2(\theta))=1+\cos(\theta) \\ 33\cos^2(\theta)=1+\cos(\theta)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0if you want replace cos(theta) with u for now \[33u^2=1+u\] solve for u

freckles
 one year ago
Best ResponseYou've already chosen the best response.0by first putting everything on one side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i have a range to follow

freckles
 one year ago
Best ResponseYou've already chosen the best response.0hmmm how did you get u=1?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0\[33u^2=1+u \\ \text{ add } 3u^2 \text{ and subtract } 3 \text{ on both sides } \\ 0=3u^2+u+13 \\ 0=3u^2+u2 \\ 0=(3u2)(u+1)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.0neither u+1=0 or 3u2=0 leads to u=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.0but 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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