Question

Sketch the graph of a periodic function whose period is 10 and has a range {y| 4 ≤ y ≤ 10, y ε R}.

Answer 1

the period \(T\) of a trigonometric function of the form\[A\sin(Bx+C)\text{ or }A\cos(Bx+C)\]is given by\[T=\frac{2\pi}{|B|}\]so write any equation with \(B\) such that \(T=10\)

also note that the amplitude of the waves above are \(A\)

then we need to shift the graph up so it falls between y=4 and y=10 at all times
what is the amplitude if those are the bounds?