### 15.2. Manual Graphing of the Sine Wave

#### 15.2.1. Plotting Point Pairs

We can graph any curve, including the sine wave, by computing and plotting point pairs, as we did for other functions.

## Example 7:Given the sine function - y = 3.2 sin(2x − 46°)
find the amplitude, period, frequency, and phase shift. Make a graph of at least one cycle by computing and plotting point pairs. Solution: The constants in the equation are - a = 3.2 b = 2 c = −46°
Therefore, Let us compute points from x = − 15° to 195°, in steps of 15°. These points are plotted in Fig. 15-8 and connected with a smooth curve. For comparison, we show a calculator screen. TI-83/84 calculator check for Example 7 y = 3.2 sin(2x − 46°). Tick marks on the x axis are 30° apart. ## Figure 15.8. FIGURE 15-8 |

#### 15.2.2. Quick Manual Graph of the Sine Wave

As shown in the preceding example, we can plot any curve by computing and plotting a set of point pairs. But a faster way to get a sketch is to first draw a rectangle whose height is twice the amplitude a and whose width equals the period P. Then sketch the sine curve (whose shape does ...

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