What is the shift along x of the trig function y = cos(4x/3 minus 1)?

Any link of proof would be appreciated if you have one

Thank you

To find the shift along the x-axis of the trigonometric function y = cos(4x/3 - 1), we can compare it to the standard cosine function y = cos(x).

The general equation for a cosine function can be written as y = A * cos(Bx + C) + D, with A representing the amplitude, B representing the period (or frequency), C representing the phase shift along the x-axis, and D representing the vertical shift.

In this case, the given function is y = cos(4x/3 - 1), where we can observe that B = 4/3.

The phase shift, C, in the general cosine function equation is given by C = -φ/B, where φ represents the phase shift in radians. In this case, -φ = -1, so C = -1 / (4/3) = -3/4.

Therefore, the shift along the x-axis for the function y = cos(4x/3 - 1) is -3/4 units to the right.

As for a proof or further explanation, you can refer to trigonometry textbooks or online resources that cover the topic of trigonometric functions and their properties.