Answer to Question #158157 in Geometry for Bryell

Question #158157

Find the length of the arc on the unit circle with the given central angles

a. 315º

b. 240º


1
Expert's answer
2021-01-26T02:34:44-0500

"Since\\:it\\:is\\:a\\:unit\\:circle\\:its\\:radius\\:is\\:one\\:unit".

"The\\:circumfrence\\:2\\pi r\\:is\\:simplified\\:to\\:2\\pi ."

"\\left(a\\right)\\:\\:\\frac{arc\\:length}{circumfrence}=\\frac{central\\:angle}{360^{\\circ }}"

"\\frac{arc\\:length}{2\\pi }=\\frac{315^{\\circ }}{360^{\\circ }}"

"arc\\:length=\\frac{315\\times2\\pi }{360}"

"arc\\:length=\\frac{7}{4}\\pi"


"\\left(b\\right)\\:\\:\\frac{arc\\:length}{circumfrence}=\\frac{central\\:angle}{360^{\\circ }}"

"\\frac{arc\\:length}{2\\pi }=\\frac{240^{\\circ }}{360^{\\circ }}\\:"

"\\:arc\\:length=\\frac{240\\times2\\pi }{360}"

"arc\\:length=\\frac{4}{3}\\pi"





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