Consider the two functions and

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider the two functions f(x)=sin⁡3xf(x)=\sin 3x and g(x)=sin⁡(3x+π3)g(x)=\sin\left(3x+\dfrac{\pi}{3}\right). (i) Sketch, on the same axes, one complete period of each function. (ii) Determine the phase difference between the two graphs and state which function leads the other. (iii) Solve f(x)=g(x)f(x)=g(x) for 0≤x≤2π0\le x\le 2\pi. (iv) Comment briefly on how the horizontal shift influences the points of intersection of the two graphs.

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