Answer to Question #5904 in Trigonometry for Shelby

Question

cos(5theta - pie/6) = -square root 2/ 2

Answer 1

cos(5theta - pie/6) = -square root( 2)/ 2

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



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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