Trignometric functions and identities

  • Thread starter nil1996
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  • #1
nil1996
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Homework Statement


How to quickly solve problems on maximum and minimum values of trig functions with help of calculus:
Ex. 10cos2x-6sinxcosx+2sin2x


Homework Equations


none


The Attempt at a Solution


I know the method of simplification. But i want to do it quickly with calculus. How to do that??
 
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Answers and Replies

  • #2
HallsofIvy
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If you "want to do it quickly with calculus" then take the derivative, set the derivative equal to 0, and solve for x. However, the derivative is fairly complicated and I'm not sure this is "quicker" than just completing the square in the original.

Setting [itex]f(x)= 10cos^2(x)- 6sin(x)cos(x)+ 2sin^2(x)[/itex] then [itex]f'(x)= -20cos(x)sin(x)- 6cos^2(x)+ 6sin^2(x)+ 4sin(x)cos(x)= -16sin(x)cos(x)- 6(sin^2(x)- cos^2(x))= 0[/itex].
 
  • #3
nil1996
301
7
OK. but we get maximum values from that what about minimum values?
 

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