tammyhawatmeh
cos θ = − root2 /2
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baldymcgee6
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how can you get rid of the cosine?
tammyhawatmeh
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arc cos?
baldymcgee6
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yep
baldymcgee6
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do you know the unit circle?
tammyhawatmeh
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yup
baldymcgee6
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okay, so where is cos(θ) = -sqrt(2/2) ?
tammyhawatmeh
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3pi/4
baldymcgee6
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Yes.. correct.
hartnn
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what about 5pi/4 ?
hartnn
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now do u need general solution or within the range 0 to 2pi ?
tammyhawatmeh
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these are the directionsSolve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
hartnn
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means genearalized solution, can u generalize this ?
tammyhawatmeh
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5pi/4 ,-5pi/4,3pi/4,-3pi/4
baldymcgee6
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There is an infinite amount of solutions, you need to write it in a way to GENERALIZE the solution.
hartnn
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so let me generalize it.
cos function is periodic with 2pi.
so values repeat after every 2pi*k
here,
\(\theta =\pm(3\pi/4+2\pi k),\pm(5\pi/4+2\pi k)\)
tammyhawatmeh
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ohh i see but why do u add the 2pik at the end ? because it is a periodic function?
hartnn
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yes, as i said cos function is periodic with 2pi.
so if a is solution, so is a+2pi, a-2pi,a+4pi,a-4pi, and so on
tammyhawatmeh
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ohh i see i missed this whole lesson on this section and i dont know any of it