What is the shift along y of the trig function y = cos(4x/3 minus 1)?
Any link of proof would be appreciated if you have one
Thank you
To determine the shift along the y-axis of the trigonometric function y = cos(4x/3 - 1), you need to examine the expression "-1" in the function.
The general formula for the shift along the y-axis of a trigonometric function is given by y = cos(ax + b) + c. In this formula:
- "a" represents the period of the function (i.e., how quickly it repeats itself);
- "b" represents the phase shift along the x-axis;
- "c" represents the shift along the y-axis.
In the given function, y = cos(4x/3 - 1), we are interested in determining the shift along the y-axis, which is denoted by "c."
The value of "c" in this case is "-1" since it is outside the cosine function. Therefore, the shift along the y-axis for this function is -1.
To visualize this, you can plot the graph of y = cos(4x/3 - 1). The entire graph would be shifted downwards by 1 unit compared to the basic cosine graph y = cos(4x/3).
As for a proof or more detailed explanation, you can refer to trigonometric textbooks, online educational resources, or mathematics websites like Khan Academy or Math Planet. These sources provide step-by-step explanations and proofs for various trigonometric function transformations.