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# Annotations 2

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Annotations 2 of Developing Expert Voices

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### Annotations 2

1. 1. Annotations 2 Tides
2. 2. Slide 1 a.) <ul><li>First we must remember DABC, the order in which we follow to make sketching trig functions easy. D - the vertical shift or sinusoidal axis of the graph; the graph “wraps” around this line. It is the average value of the graph. A - the amplitude that determines the stretch of the graph. If it is negative, the graph is inverted; flipped horizontally over the y-axis. If positive, Sine graphs will start at zero, and Cosine graphs will start at its max value, which is one. B - represents a factor that influences the period of the graph. This is used to determine the scale values of the x-axis. C - represents the horizontal shift of the graph. </li></ul>
3. 3. Slide 1 a.)Continued <ul><li>D is equal to 0 because the sinusoidal axis is on y=0 and the average sea level is at 0 feet </li></ul><ul><li>A is equal to 2 so the graph will have its maximum and minimum values 2 units away from the sinusoidal axis </li></ul><ul><li>The period is 12.5 hours so the scale of the graph will include four main values: 12.5(the period), 9.375(3/4 period), 6.25(half period), and 3.125(1/4 period) </li></ul><ul><li>We know that the graph has a max on Jan 1 st so we can start the graph on the y-axis </li></ul><ul><li>Don’t forgot to place arrows on the ends of the x and y axis, and on the ends of the graph </li></ul><ul><li>Remember to label the axis: the x-axis represents the independent factor (time in hours) and the y-axis represents the dependent factor (height is feet) </li></ul>
4. 4. Slide 2 b.) <ul><li>Note that there are endless possibilities of equations for sine and cosine graphs </li></ul><ul><li>First we must find the four components: A, B, C, and D of the equation: </li></ul><ul><li>In this graph A is always 2, however the sign of A depends on where you begin </li></ul><ul><li>B is determined by the equation: </li></ul><ul><li>C is the horizontal shift from the y-axis (the starting point of the trig functions without any translations) and depends on where you begin </li></ul><ul><li>D is the sinusoidal axis and is determined by finding the distance between the max and the min and dividing that value by 2. </li></ul>
5. 5. Slide 3 c.) <ul><li>First we choose any one of the equations we created; ideally the most simple equation for easy use. In this case, I used: </li></ul><ul><li>Next, we let and solve for theta </li></ul><ul><li>After algebraically solving for theta, we find that there are 2 solutions for theta. However, since the question states the first time on January 1 st , we choose the lowest value. </li></ul><ul><li>Now we input our theta value back into the equation: and solve for t, the time in hours </li></ul><ul><li>Then we subtract 1 (the hour) and multiply that difference by 60 (number of minutes in one hour) to find the time in minutes </li></ul><ul><li>Our final answer is 1:47 a.m. (1.7819 hours passed 12:00 a.m.) </li></ul>