Question

Write the equation of a sine or cosine function to describe the graph.

Answer 1

Explanation:

first of all the graph is shifted up by 1 then we should add 1 to the function we have.

after that its obvious that the function is sine because if we remove the 1 we add it then it will be 0 when the angle is 0.

the function we have now is y = 1 + sin(ax).

to know the value of a we choose an angle we already know its sine for example:

2 = 1 + sin(a * 1/8)

1 = sin(a * 1/8)

sin-1(1) = PI/2 = a*1/8 => PI = 180

a = 4 * PI

at the end we will have => y = 1 + sin(4PI * x).