The function f is such thatfx)a-bcosx for 0<x<360, where a and b are positive constants .the maximum value of fx is 10 and minimum is-2 find a and b?

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Answer 1 · 2017-11-14T21:41:47

$color(blue)(a=4)$

$color(blue)(b=6)$

Note:

You have to include $0$ in the interval, because this is where the minimum value of $-2$ occurs. So interval should be:

$0<=x<360^o$

$f(x)=a-bcosx$

For interval $0 <= x < 360^o$ , the greatest value of $cosx=1$ . This occurs when $x=0^o$ the minimum value of $cosx= -1$ this occurs when $x=180^o$

So maximum value:

$a-bcos(180)= 10$

$a-b(-1)=10$

$a+b=10$ $color(white)(88)[1]$

Minimum value:

$a-bcos(0)=-2$

$a-b(1)=-2$

$a-b=-2$ $color(white)(88)[2]$

Solve $[1] and [2]$ simultaneously:

Subtract [2] from [1]:

$a+b=10$
$a-b=-2$

$2b=12=>b=6$

using [2]:

$a-6=-2=>a=4$

$:.$

$color(blue)(a=4)$

$color(blue)(b=6)$