Question

How do you figure out the range of f(x)=7+3cosx+4sinx for the range 0<=x<=2pi
? I know the answer is 2 to 12 but I don't know how to get there

Answer 1

cos and sin vary between -1 and 1 so test the extremes.

Answer 2

@coconutshake
If you ever have
\[y= A\cos x+B\sin x\]
Then max and min value of y are given as
\[max= \sqrt {A^2+B^2}\]
\[min= -\sqrt {A^2+B^2}\]
Can you find now?

Answer 3

if you R wich is the amplitude the range will be
\[R+7<f(x)<-R+7\]
\[5\cos (\theta-53,1^{0})\]
\[5+7<f(x)<-5+7\]
\[12<f(x)<-2\]