ࡱ> M 0bjbj== >WW+(l   8N b ,M(  : " v!v!v!'''''''$W) w+n'v! lv!v!v!'# (###v!  '#v!'##'@' Ҙ   j" ''$(0M('+v#4+'#Named Ranges 4 Animating the Construction of a Cosine Graph Open Excel and save the new file as Cosine on your floppy disk. Centre Justify all Cells. In Cell A30 type a, in Cell B30 type x and in Cell C30 type y. Then in Cell A31 type 0 and select Edit ( Fill ( Series, and fill in the details as shown below. Click in Cell A31 and let go of the mouse button, then use the scrollbar to scroll down to the end of the a column of data at A103. Next hold down the Shift button on the keyboard then click once in Cell A103. This selects the range A31:A103, and avoids overshooting the highlighting process if the left mouse button is held down and moved to the bottom of the screen. With this range highlighted click once in the Name Box and type a and press Return to enter this Range Name. In Cell B31 type in = cos(radians(a)), and press Return, the Cell should show a value of 1 now, notice that trig arguments must be in radians either directly or by a conversion as used above . In Cell C31 type in = sin(radians(a)), and press Return, this Cell should show a value of 0. Highlight Cells B31 to C31 and then double click the selections fill handle to calculate values down at all values of a. Highlight the Range B31:B103 and with this range highlighted click once in the Name Box and type x and press Return to enter this Range Name. Highlight the Range C31:C103 and with this range highlighted click once in the Name Box and type y and press Return to enter this Range Name. Now without any of the a, x or y ranges selected click on the Chart Wizard icon in the Standard Toolbar. Next, in the 1st Chart Wizard window Standard Types Tab, double click on the XY (Scatter) picture and then on the smooth curve without data points present.  Click Next and in the Data Range Tab of the following Dialogue Box in the Data Range Input Box just type x,y and press Next. This will automatically select the required x-y range for the graph. Now continue to set the remaining graph options so that no titles, keys or axes names are showing i.e. a bare graph of a circle! Next, resize the graph so that it covers the Cells A2:E20 Notice that if you hold down the Alt button whilst moving or resizing then the graph will Snap-to the spreadsheet gridlines. Right click anywhere on the background shading of the graph and then select Format Plot Area, from the drop down menu. Then in the Area frame click on None to remove the background shading, also right click on any single horizontal, graph Gridline and from the drop down menu select Clear. In Cell B22 type driver, Cell D22 type circle, Cell F22 type graph and I22 type pie From Cell B23 to G23 type, t, inc, xc, yc, ag and yg in each respective Cell. Highlight Cells B23 to C24 and select Insert ( Name ( Create, etc, to Name the respective Cells Next select Tools ( Options( Calculation Tab, and set up the Dialogue Box as shown below which sets up the spreadsheet to deal with circular references: Notice again, that the value in the Maximum change text box is unimportant to the present set up, as are the Workbook options, so they can be left with whatever default values they have. Put the numerical value 2 in Cell C24 and in Cell B24 type = mod(t + inc, 360), and press Return. The number value of inc is a speed control for the graph automation. In Cell D24 type in = cos(radians(t)), and in Cell E24 type in = sin(radians(t)). In Cell D25 type in 0, and in Cell E25 also type in 0. In Cell D26 type in = cos(radians(t)), and in Cell E26 type in = sin(radians(t)). In Cell D27 type in 0 and in Cell E27 type in = sin(radians(t)). In each of Cells F24, F25 and F27 type in = t, and in Cell F26 type in the numerical value 0. In Cell G24 type in =cos(radians(t)), and in each of Cells G25, G26 and G27 type in the numerical value 0. In Cell I23 type in = 360 EMBED Equation.DSMT4 t, and in Cell I24 type in = t. Highlight Cells D24 to E25 and press Ctrl+C to copy, then click once, anywhere on the graph and select Edit ( Paste Special. From the Paste Special Dialogue Box choose the options shown checked below. Repeat this process but with Cells D26 to E27. What should have been drawn are a radius line and a horizontal line from the tip of the radius on the circumference of the unit circle to the y-axis. The length of this horizontal line is in fact the value of the Cosine of the angle that the radius makes with the positive x-axis. Let us now adjust the colours of these lines before moving on. First click anywhere on the graph then select the radius line with a double mouse click. This opens the Format Data Series Dialogue Box, in the Patterns Tab select Color and change to red. Similarly, change the colour of the horizontal line to bright green. Press and hold down the F9 Special Function key to recalculate the worksheet and produce the appearance of motion of the radius. We now draw the more familiar Cosine Graph as follows Without any of the a, x or y ranges selected click on the Chart Wizard icon in the Standard Toolbar. Next, in the 1st Chart Wizard window Standard Types Tab, double click on the XY (Scatter) picture and then on the smooth curve without data points present. Click Next and in the Data Range Tab of the following Dialogue Box in the Data Range Input Box just type a, x and press Next. This will automatically select the required x-y range for the graph. Now continue to set the remaining graph options so that no titles, keys or axes names are showing i.e. a bare graph of a the standard Cosine curve! Next, resize the graph so that its depth spans the same number of vertical Cells as the previous graph, the left border of this graph should therefore now occupy the Cells F2:F20 Recall again, that if you hold down the Alt button whilst moving or resizing then the graph will Snap-to the spreadsheet gridlines. Make the graph as wide as your screen will allow. Once again, right click anywhere on the background fill in the graph and select Format Plot Area, from the drop down menu. Then in the Area frame click on None to remove the background shading, also right click on any single horizontal, graph Gridline and from the drop down menu select Clear. The horizontal axis will probably go up to 400, if so then double click on it and from the Format Axis Dialogue Box choose the Scale Tab. Change the Maximum to 360 and the Major unit to 90 then click OK. Highlight Cells F24 to G25 and press Ctrl+C to copy, then click once, anywhere on the Cosine graph and select Edit ( Paste Special. From the Paste Special Dialogue Box choose the options shown checked below. Repeat this process but with Cells F26 to G27. What should have been drawn are a vertical line from the x-axis to the curve and a horizontal line from origin to the base of the vertical line. The length of this vertical line is the value of the Cosine at the angle that is shown by the horizontal line, this being related to the angle swung through in the first graph by the radius. Press and hold down the Special Function Key F9 to see both graphs animated. Finishing Touch An Animated Angle Highlight the Cells I23 to I24, type pie into the Name Box and press Return. Next click into any empty Cell and then click on the Chart Wizard on the Standard Toolbar. From Step 1 choose the Doughnut Chart Type and click Next. From Step 2 just type pie into the Data range box and click Next. From Step 3 remove the Legend and Data Labels and then click on Finish. You should then have a chart that looks similar to the following one below. If it doesnt then press the Special Function Key F9 until the radius arm in the first graph lies somewhere in the first quadrant.  Then click anywhere in this graph once then use either the right or the left cursor arrows on the keyboard to alter the selected item within the graph. Stop when you get to the picture on the right and NOT the picture on the left below.   Now, with the handles visible in the larger slice, right click in this slice as shown above. From the Drop Down Menu click on Format Data Point, click on the Patterns Tab and then select the None for both the Border and the Area options. Next from the Options Tab alter the Angle to  EMBED Equation.DSMT4  and the Doughnut size to  EMBED Equation.DSMT4  as shown below, then click on OK. At this stage the doughnut should still be quite sizable relative to the worksheet we will now need to reduce it in size. However, before reducing this Doughnut graph we return to our first graph of the Unit Circle to remove its background colours. Right mouse button click once anywhere on the Unit Circle graph and from the Drop Down Menu click on Format Chart Area. Click on the Patterns Tab and then select the None for both the Border and the Area options, then click OK. The Gridlines of the worksheet should now be visible through this graph now, however they will be removed later. Returning to the Doughnut graph, left click once close to the outer border, but still within the graph, to select it and to display the resizing handles. Then position the mouse over any corner resize handle. In this position, press and hold down the left mouse button and drag the mouse until the Doughnut lies within a square frame of approximately 2cm side length. With the frame selected click the right mouse button and from the Drop Down Menu click on Format Chart Area (or Format Plot Area), click on the Patterns Tab and then select the None for both the Border and the Area options. Again, the Gridlines of the worksheet should be visible through this graph too. Next with the Doughnut graph selected click and hold down the left mouse button, then drag the Doughnut until it lies at the centre of the first, Circle graph. You may need to experiment slightly to get the two graphs precisely aligned at a common origin. Once you are satisfied click anywhere on the worksheet to de-select the graphs and press the Special Function Key F9 several times to observe the animation. To show some consistency between the graphs it is advisable to make all related lines the same colour in respective graphs, for instance: The Doughnut colour should be the same colour as the line that extends from the origin to the angle value in the standard Cosine graph, etc. Recall that selecting graph objects is most easily done via the Keyboard Arrow Keys first then double clicking on the, already selected, objects with the left mouse button to Open the Format Data Series Dialogue Box from which most things can be modified in some way to suit your needs. To prevent accidental, relative movement of the respective graphs hold in the Shift button whilst clicking once on each graph then, once all are simultaneously selected, right click within any graph and from the Drop Down Menu select Grouping ( Group. Finally we remove the worksheet Gridlines by selecting Tool ( Options ( View Tab, and un-checking the Gridlines Window Option Box. 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