Question

Plz help me with this

Answer 1

Answer:
`\bold{A)\quad y=5sin\bigg((6)/(5)x-\pi\bigg)-4}`

Explanation:

The general form of a sin/cos function is: y = A sin/cos (Bx-C) + D where the period (P) = 2π ÷ B

In the given function,
`B=(6)/(5)` →
`P=2\pi \cdot (5)/(6)=(10\pi)/(3)`

Half of that period is:
`(1)/(2)\cdot (10\pi)/(3)=\large\boxed{(5\pi)/(3)}`

Calculate the period for each of the options to find a match:

`A)\quad B=(6)/(5):\quad 2\pi / (6)/(5)=2\pi \cdot (5)/(6)=(5\pi)/(3)\quad \leftarrow\text{THIS WORKS!}\\\\\\B)\quad B=(6)/(10):\quad 2\pi / (6)/(10)=2\pi \cdot (10)/(6)=(10\pi)/(3)\\\\\\C)\quad B=(5)/(6):\quad 2\pi / (5)/(6)=2\pi \cdot (6)/(5)=(12\pi)/(5)\\\\\\D)\quad B=(3)/(10):\quad 2\pi / (3)/(10)=2\pi \cdot (10)/(3)=(20\pi)/(3)`