The question is:
State the vertical shift and the equation of the midline for y = 4cosθ-1?
I have NO idea what to do here. Can someone possibly show me step by step? I am more of a visual learner, if I see something done I can usually understand it.
Sure! I'd be happy to walk you through the steps to find the vertical shift and equation of the midline for the given equation y = 4cosθ - 1.
Step 1: Understanding the Form of the Equation
In the given equation, y = 4cosθ - 1, the "cosθ" term indicates that it is a cosine function, where θ represents the angle. The constant term "-1" shifts the graph vertically downward by one unit.
Step 2: Identifying the Vertical Shift
To find the vertical shift, we need to determine how much the graph has been shifted up or down. In this case, -1 indicates that the graph has been shifted downward by one unit.
Step 3: Determining the Equation of the Midline
The midline is a horizontal line that represents the average value of the function. For a cosine function, the equation of the midline is given by the constant term in the equation. In this case, the equation of the midline is y = -1.
To summarize:
- The vertical shift is -1 unit (shifted downward).
- The equation of the midline is y = -1.
Visually, you can imagine the cosine function starting at the midline (y = -1) and then oscillating above and below it, reaching its maximum and minimum values based on the amplitude and period of the function.
I hope this helps! Let me know if you have any further questions.