Chapter 13.8, Problem 37PPS

To determine

Find the equation by using the given terms.

Answer to Problem 37PPS

The equation is $y=\sin (x-4)+3$ .

Explanation of Solution

Given: It is given in the question that the base equation is $y=\sin x$ and four units to the right and three units up.

Concept Used:

In this, use the concept of general equation for sine $y=\sin (\theta -h)+d$ where h is phase shift and d is vertical shift and h units to the right if h is positive or h units to the left if h is negative.

Calculation: Here, let the equation be $y=\sin (\theta -h)+d$ .

Since, in this the phase shift is four units to the right, so $h=4$

And the vertical shift d units up if d is positive or d down if d is negative.

In this, case the vertical shift is three units up, so $d=3$ .

So, from the above put the values in the equation,

  $y=\sin (x-4)+3$ .

Conclusion:

The equation is $y=\sin (x-4)+3$ .