Solved: For individual or collaborative investigation (Exercises 6366) Connecting the

Chapter 4, Problem 66

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For individual or collaborative investigation (Exercises 6366) Connecting the Unit Circle and Sine Graph Using a TI-84 Plus calculator, adjust the settings to correspond to the following screens. MODE FORMAT Y = EDITOR 4.2 Translations of the Graphs of the Sine and Cosine Functions Horizontal Translations The graph of the function y = 1x d2 is translated horizontally compared to the graph of y = 1x2. The translation is d units to the right if d 7 0 and ' d ' units to the left if d 6 0. See Figure 12. With circular functions, a horizontal translation is a phase shift. In the function y = 1x - d2, the expression x - d is the argument. Horizontal Translations Vertical Translations Combinations of Translations A Trigonometric Model y y = f(x) 3 0 x 4 y = f(x + 3) y = f(x 4) Horizontal translations of y = f(x) Figure 12 Graph the two equations (which are in parametric form), and watch as the unit circle and the sine function are graphed simultaneously. Press the TRACE key once to obtain the screen shown on the left below. Then press the up-arrow key to obtain the screen shown on the right below. The screen on the left gives a unit circle interpretation of cos 0 = 1 and sin 0 = 0. The screen on the right gives a rectangular coordinate graph interpretation of sin 0 = 0. Explain the relationship between the coordinates of the unit circle and the coordinates of the sine and cosine graphs.