User manual TERRAILLON WEATHER STATION SOLSTICE

[. . . ] Installing this application requires TIGRAPH LINKË software and link cable. After you enter the store, follow the links to Computer Software, then TI-GRAPH LINK. You can download a free copy of the latest version of TIGRAPH LINK software from the software section of education. ti. com. Follow the links to Connectivity Software, then TI-GRAPH LINK. TI-83 Plus Conic Graphing Page 3 What is Conic Graphing? Conic Graphing is a TI83 Plus calculator software application that you can use to graph the four basic conic sections. [. . . ] Select an equation for the conic section. Tip A conic section may have more than one equation option for each mode. If an arrow appears below the equation number, you can press h to see more equations. TI-83 Plus Conic Graphing Page 21 4. The fixed point is the center of the circle; the constant distance is the radius. (X-2) 2 + (Y-2) 2 = 25: Center (2, 2) Radius 5 Calculator mode Function Equations (X1H) 2 + (Y1K) 2 = R 2 AX2 + AY2 + BX + CY+ D = 0 Parametric X = R cos (T) + H Y = R sin (T) + K Polar R = 2A cos (T) R = 2A sin (T) A 2 = B 2 + R 2 1 2BR cos (T1b) TI-83 Plus Conic Graphing Page 26 Example Graph an arc of a circle with radius = 8 whose center is at (0, 0), using parametric mode. Note To complete this exercise, you need to set your calculator to radian mode before you start the Conic Graphing application. Select MAN so that you can manually change window settings. TI-83 Plus Conic Graphing Page 27 6. Enter the values for H, K, and R [(0, 0) and 8], as defined in the problem. (Otherwise, the circle may look like an ellipse. ) The graph of the circle is drawn. 11. Change the following parameters: Tmin = 0 S Tmax = (In degree mode, Tmax = 90. To change to degree 2 mode, you must exit Conic Graphing. ) TI-83 Plus Conic Graphing Page 28 13. You can change the Tmin and Tmax values to display the graph of the arcs in different quadrants. TI-83 Plus Conic Graphing Page 29 Ellipses Definition An ellipse is the set of points whose distances from two fixed points in the plane have a constant sum. The line through the foci of an ellipse is the ellipse's focal axis. The graph of the shape of the shadow is drawn. TI-83 Plus Conic Graphing Page 39 Parabolas Definition A set that consists of all the points in a plane equidistant from a given fixed point and a given fixed line in the plane is a parabola. (Y12) 2 = 8 (X13): 2ep R = 11e cos (T) 2ep R = 1+e cos (T) 2ep R = 11e sin (T) 2ep R = 1+e sin (T) Calculator mode Function Equations (Y1K) 2 = 4P(X1H) (X1H) 2 = 4P(Y1K) Parametric X = AT2 + H Y=T+K X=T+H Y = AT2 + K Directrix X=1 Vertex (3, 2) Polar Focal axis Focus (5, 2) TI-83 Plus Conic Graphing Page 40 Example Given the equation of projectile motion and necessary values, find the focus and directrix of the path of the projectile (parabola). Assume a ball is thrown with a velocity of 65 ft/sec at an angle of T = tan11 (3/4). Assume that the gravitational force is g = 32 ft/sec 2. Equations of a projectile in motion: X = V 0 cos (T) T 1 Y= V 0 sin (T) T 1 2 GT2 Givens: V 0 = 65 ft/sec G = 32 ft/sec 2 From T = tan11 (3/4): 4 cos (T) = 5 3 sin (T) = 5 TI-83 Plus Conic Graphing Page 41 Steps: 1. 4   X = 65  5  T X = 52T, then X T = 52 , then 3  1     Y = 65  5  T 1  2  32 T2, then Y = 39T 1 16T2 2  X  X     X Substitute 52 for T: Y = 39  52  1 16  52  507  1521    X Y  8  = 1 169  64  Complete the square:  2 2 2. Select PAR to change the mode to parametric. TI-83 Plus Conic Graphing Page 42 6. Press R to escape from the graph screen. TI-83 Plus Conic Graphing Page 43 13. Xmin = 0 Xmax = 125 Xscl = 5 Ymin = 0 Ymax = 25 Yscl = 5 TI-83 Plus Conic Graphing Page 44 16. Press U to trace the trajectory. TI-83 Plus Conic Graphing Page 45 Glossary Term Asymptote Definition A straight line associated with a curve such that as a point moves along an infinite branch of the curve, the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line. A point that is related to a geometrical figure in such a way that for any point on the figure there is another point on the figure such that a straight line joining the two points is bisected by the original point. A closed plane curve in a plane whose distance from a given fixed point in the plane is constant. [. . . ] The problem is usually associated with the TIGRAPH LINK cable and its connection to the TI83 Plus and/or to the computer. Make sure the cable is firmly inserted in the calculator I/O port and the computer. If this does not correct the problem, try a different TIGRAPH LINK cable and reboot your computer. If you continue to get this error, please contact TICaresË Customer Support for assistance. Calculator to Calculator Communication Error This problem is usually associated with the unit-to-unit cable and its connection between the TI83 Plus calculators. [. . . ]