Chapter 12.8, Problem 38PPS

To determine

Find the equation by using the given terms.

Answer to Problem 38PPS

The equation is $y=\cos (x+5)-2$ .

Explanation of Solution

Given: It is given in the question that the base equation is $y=\cos x$ and five units to the left and two units down.

Concept Used:

In this, use the concept of general equation for cosine $y=\cos (\theta -h)+d$ 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 $y=\cos (\theta -h)+d$ .

Since, in this the phase shift is five units to the left, so $h=-5$ .

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 two units down, so $d=-2$ .

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

  $y=\cos (x+5)-2$ .

Conclusion:

The equation is $y=\cos (x+5)-2$ .