Question

Please help me solve this! I’ve been stuck for ages! Thankyou

Answer 1

The equation of graph G is y = sin(x- π/2).

Translating the Sine Function

The graph of y = sin x° is translated to give graph G. This means that the basic sine function has been shifted horizontally and/or vertically.

Here's how to determine the equation of graph G:

1. Identify the horizontal shift:

The original function is y = sin x°.

Graph G appears to be shifted π/2 units to the right.

2. Identify the vertical shift:

The original function crosses the y-axis at y = 0.

Graph G appears to be shifted down 1 unit.

We know this because sines are periodic functions with a period T = 2*pi

3. Combine the shifts:

Since the horizontal shift is to the right, we need to subtract π/2 from the argument of the sine function.

Since the vertical shift is downwards, we need to subtract 1 from the function.

Therefore, the equation of graph G is: y = sin(x- π/2)

Answer 2

y = sin(x- pi/2)

Explanation:

Please see the attached image to see your graphs.

By simple inspection we can see that the sine is shifted pi/2 to the right.

We know this because sines are periodic functions with a period T = 2*pi

We can also see that the maximum point of the graph (y = 1) got shifted by a fourth of the period.

And finally, since we want to shift the graph to the right, we need to substract from the argument of the sine term.