Because the temperature ranges from 70° to 74°, the amplitude of the sine curve is 2. Because the temperature goes from its maximum of 74° back to 74° in 4 minutes, the period is 4. Since the period is 2π/B, we get B = π/2. Now concentrate on one cycle of the function. Starting at (13, 72) the temperature increases to its maximum of 74°, decreases to its minimum of 70°, and then ends in the middle at (17, 72). We choose this cycle because it duplicates the behavior of y = sin(x) on its fundamental cycle [0, 2π]. So shifting y = sin(x) to the right 13 and up 72 gives us y=2 \sin \left[\frac{\pi}{2}(x-13)\right]+72. Its graph is shown in Fig. 5.58. Changing this equation with any right or left shift by a multiple of 4 gives an equivalent equation. For example, y=2 \sin \left[\frac{\pi}{2}(x-1)\right]+72 is an equivalent equation.