C3 Trig

Q: a) Find minimum value of 12cosx - 4sin x

b) Find the smallest possible value for x for which this minimum value occurs

Q's previous to these, if needed worked out as 4rt10 cos (x + 18.43) , the original equation was f(x) = 12cosx - 4sinx.

R = 4rt10
Alpha = 18.43

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I don't know the way to work out min's of these stuff, so if someone could explain the whys and hows i would greatly appreciate it, +rep too.

Thanks :smile:

Reply 1

Kolya

Do you know how cosx is transformed if we have acosx , for some constant a? How about if we have cos(x-a)? Do you know how that will change the shape/position of the cosx graph?

Reply 2

Mos Def

Yeah, the a is the factor it stretches by, and cos(x-a), means it shifts a units to the right...

so im guessing it stretches by 4rt10 and shifts to the left by 18.43 :s-smilie:

Reply 3

fusionskd

T_Bag

Yeah, the a is the factor it stretches by, and cos(x-a), means it shifts a units to the right...

so im guessing it stretches by 4rt10 and shifts to the left by 18.43 :s-smilie:

The minimum value for cos and sin is -1. [max value is 1]

In this case all you need to do is equate 4rt10 cos (x + 18.43) to -4rt10 and find the value of x.

Thats all :biggrin:

Reply 4

The Bachelor

The minimum value of cos is -1, so the minimum value of 4rt10 cos (x + 18.43) is -4rt10.

So solve for x: $-4\sqrt 10 = 4 \sqrt 10 \cos (x + 18.43)$

Reply 5

Mos Def

ohh i get it, were looking at the graph, and obviously the lowest value will be the dip which is normally -1, but is now -4rt10.

+rep to you lot :smile:

Reply 6