Question

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.

Amplitude 5, period 6, point (2, 0)

Answer 1

d

Explanation:

edge2021

Answer 2

`y = 5\sin( (\pi)/(3) x - (2\pi)/(3) )`

EXPLANATION

Let the equation of the sine curve be of the form;

`y = a \sin(bx + c)`

where a=5 is the amplitude and period,

`(2\pi)/(b) = 6`

This implies that

`b = (2\pi)/(6)`

`b = (\pi)/(3)`

We substitute the values we got so far into our equation to obtain;

`y = 5\sin( (\pi)/(3) x + c)`

When we substitute (2,0) we obtain;

`0= 5\sin( (2\pi)/(3) + c)`

Solve for c.

`\sin( (2\pi)/(3) + c) = 0`

`(2\pi)/(3) + c = \sin^( - 1) (0)`

`(2\pi)/(3) + c = 0`

`c = - (2\pi)/(3)`

Hence our equation becomes

`y = 5\sin( (\pi)/(3) x - (2\pi)/(3) )`

The correct choice is D.