Question

Which of the following functions has an amplitude of 5 and passes through the point (0,0)?

a. 5 cos (pi)x
b. -5 sin x
c. -5 cos x
d. sin (pi)x

Answer 1

You know that

`\sin 0=0, \\ \cos 0=1`.

Then it should be the sine function.

If
`y=-5 \sin x`, then
`y(0)=-5 \sin 0=-5\cdot 0=0` and this function has amplitude 5, because
`y((3\pi)/(2))=-5 \sin (3\pi)/(2)=-5\cdot (-1)=5`.

If
`y=\sin (\pi x)`, then
`y((1)/(2))=\sin (1)/(2)\cdot \pi=\sin (\pi)/(2)=1` and this function has amplitude 1.

Answer: Correct choice is B.