The function f is such that f(x) = a − b cos x for 0◦ ≤ x ≤ 360◦, where a and b are positive constants. The maximum value of f(x) is 10 and the minimum value is −2.

Find the values of a and b.

Question

The function f is such that f(x) = a − b cos x for 0◦ ≤ x ≤ 360◦, where a and b are positive constants. The maximum value of f(x) is 10 and the minimum value is −2.

Find the values of a and b.

alekos · Answer

have you tried to work it out ?

hartnn · Answer

think : when can f(x) be maximum ??
when cos x is minimum ? or maximum or 0  ? 

then using the appropriate value of cos x 
you can find the mim. and max. value of f(x)

lxelle · Answer

What I did was,
When cosx = -1, a-b=10 and when cosx = 1, a + b = 2. But it seems to be wrong. Help? @hartnn @alekos

hartnn · Answer

when cos x  = -1

then a+b = 10 
:)

hartnn · Answer

a- b(-1) = 10 
a+b =10

lxelle · Answer

Yup. Why is that so?

hartnn · Answer

a-b =2

lxelle · Answer

Isn't it maximum value of f(x) is 10 Hence cox(x)= 1???

hartnn · Answer

NOTE : there is -b cos x 

there is a negative sign!

when cos x is maximum, f(x) will be minimum!

lxelle · Answer

Does that mean that cos is negative?

lxelle · Answer

because it says b is a positive constant.

hartnn · Answer

b is positive

hence -b will be negative

now there is a negative quantity with cos x 

so, f(x) will not increase with cos x, it decreases with cos x
hence f(x) will reach maximum, when cos x is minimum

lxelle · Answer

Okay. Let's say the question is f(x)= a+bcos(x)
So, It'll be a-b = 10 and a+b =-2 
right?

hartnn · Answer

absolutely

lxelle · Answer

Appreciate it!:)

hartnn · Answer

^_^