SOLUTION: y=3sin(x-pi over 6)+5 for 0<x<2Pi 1) The maximum occurs when x= 2 Pi over 3 I am utterly lost as to why this is true. Pi over 6 is 30 degrees. I wondered if maybe the C

Algebra ->  Trigonometry-basics -> SOLUTION: y=3sin(x-pi over 6)+5 for 0<x<2Pi 1) The maximum occurs when x= 2 Pi over 3 I am utterly lost as to why this is true. Pi over 6 is 30 degrees. I wondered if maybe the C      Log On


   



Question 935393: y=3sin(x-pi over 6)+5 for 0 1) The maximum occurs when x= 2 Pi over 3
I am utterly lost as to why this is true.
Pi over 6 is 30 degrees.
I wondered if maybe the CAST diagram would be of relevance here?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum has to occur when the
value of the sin function = 1
That is because for all other values of
the sin function, you get a negative
value ( as much as -1 ), or you get
some positive value less than +1
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So, I can say that if I replace
+sin%28+x+-+pi%2F6+%29+ with
+sin%28+y+%29+, then +y+=+pi%2F2+ to
make the sin a maximum
-----------------------
Sop, I can say:
+pi%2F2+=+x+-+pi%2F6+
+x+=+pi%2F2+%2B+pi%2F6+
+x+=+%28+3pi+%29%2F6+%2B+pi%2F6+
+x+=+%28+4pi+%29%2F6+
+x+=+%282pi%29%2F3+
The value of the whole expression is:
+3%2A1+%2B+5+=+8+
Hope this is clear