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Answer to Question #5904 in Trigonometry for Shelby

Question #5904
cos(5theta - pie/6) = -square root 2/ 2
Expert's answer
cos(5theta - pie/6) = -square root( 2)/ 2

we'll use the following formula for roots of such equation:

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

so we obtain

5theta - pie/6=3*pie/4+2*pie*k or 5theta - pie/6=-3*pie/4+2*pie*k, where k is integer

Now we should find theta from obtained equations:

5theta =pie/6+3*pie/4+2*pie*k or 5theta =pie/6-3*pie/4+2*pie*k, where k is integer


5theta =11*pie/12+2*pie*k or 5theta =-7*pie/12+2*pie*k, where k is integer

theta =11*pie/60+(2/5)*pie*k or theta =-7*pie/60+(2/5)*pie*k, where k is integer - answer

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