00010001010008main.ACT000102000eunitcircle.EAC010000005688^[The Unit Circle and[Trigonometric Functions[\AuthorProfessor Dr. Wei-Chi Yang Department of Maths/Stats Radford University Radford, VA 24142 U.S.A. e-mail: wyang@radford.edu www.radford.edu/~wyang[[ Objective.[We shall see how we [define basic trigonometric[functions by using a unit[circle.[[Constructions.\Open and tap the +ffffg`&rYt`ffffg&rYtvrALCuxy5@  H # @6G5%`5A4  @6!A@6H  C@6xT8 BqY %@   @  R7 &1WG7 @    t@6w TvtY5Qya%Y @     5@  H# @6R#8(Yw   @6"P@H  B@6'SF %vIpuqY%@  @  Fp &1WG7 @    s@6w TvtY5Qya&Y@  @  H# @6 UGYW$3$  [Step 1. Construct a unit[circle.[Step 2. Construct a [vector on the unit circle.[*Step 3. When measuring[the Kselect ONLY the [vector whose head is [on the circle.[Step 4. Select the point[on the circle AND the [circle. Edit->Add [Animation->Go once.[Step 5. Tap the point[and select the angle, we[get a table for the [angles.[Step 6. Tap the point[and select (x,y) coordi-[nates, we get tables of[the x and y coordinates[for each point.[Step 7. Copy data from[ animation[table and then:[Step 8. Paste into [ eActivity[Step 9. Drag and drop [matrix into a 'List Editor'.[ Pasted Data:[0 0.98011478920 18.94736842 0.9270094665 0.3182427518 37.89473684 0.773448284 0.6019989634 56.84210526 0.5360719787 0.8205192464 75.78947369 0.2406039565 0.9501235373 94.7368421-0.08093723778 0.9767672003 113.6842105 -0.3937076265 0.897562981 132.6315789 -0.6638136848 0.7210938856 151.5789474 -0.8619852303 0.4664830788 170.5263158 -0.966747301 0.1613215922 189.4736842 -0.966747301 -0.1613215922 208.4210526 -0.8619852303 -0.4664830788 227.3684211 -0.6638136848 -0.7210938856 246.3157895 -0.3937076265 -0.897562981 265.2631579-0.08093723778 -0.9767672003 284.2105263 0.2406039565 -0.9501235373 303.1578947 0.5360719787 -0.8205192464 322.1052632 0.773448284 -0.6019989634 341.0526316 0.9270094665 -0.31824275180 0.98011478920\DataGraph2D Graph3D LISTCAL(, LISTSYST4NModify $ STATCALC NSTATSYS \NSequence, Sheet<| Sheet3D| SolveEq4SolveLwr8 SolveUprD StupFLG1P(StupListxD StupPict$ ViewWind y1\Hy2XHp |              $  0 !< "H #T $` %l &x ' ( ) * + , - . / 0 1 2 3 4 5 E F H I J K L M$ N0 O< PH QT R` Sl Tx ]D ^D _ D `PD a b fD gD $ 0 < H T ` l x    list3/list2system]listsystem^]=system_^system`_systema`systemb~EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE aseq_histbNewFolde system]listsystem^]=ystemEsystem]listsystem^]=systemEsystem]listsystem_]=systemEsystem]listsystem`]=systemEsystem]listsystem^]=systemEsystem]listsystem^]=systemEsystem]listsystem^]=systemEsystem]listsystem^]=systemEsystem]listsystem^]=systemEsystem]listsystem^]=systemE  0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D 0@PSheet1^Sheet2^Sheet3^Sheet4^Sheet5^SheetSheet3D i ^ $ J 3x0.980114749372*L(0.01745329456316*x+1.570795959098)-1.060926833815-7 3xP(x)`P`P``3vb3vb`(10qy`#YuY  $0<HT`lqf)r Bd S& idcE T"8  $0<HT`lx G6 xsh@hBR`WG6 G6!hBP2cxQWG@pRcG6 BR`'6!F1WPe&1W!&0xp"Rc A&1`  $0<HT`lx G 'fP sD 6xp @`9VP  7#wYpv&PYc6YaR00Y ftsY ftsYaR00Yc6Ypv&PY 7#wY@`9VP 6xp sD 'fP G  $0<HT`lx $'Q c@  QF@ P570 vvr0 V) ! 8` fH0x a2 a2 YfH0xY! 8`YV)Y vvr0Y P570Y QF@Yc@Y$'QY  $0<HT`lxC03Y x3A SUiY h Ryi`'p6B`bWP`A)7Yf% Yf% A)7 bWP 'p6B  h RyiiY`SU`x3AYC03YY $0<HT`lxG6 xsh@hBR`WG6 G6!hBP2cxQWG@pRcG6 BR`'6!F1WPe&1W!&0xp"Rc A&1` $0<HT`lx$'Q c@  QF@ P570 vvr0 V) ! 8` fH0x a2 a2 YfH0xY! 8`YV)Y vvr0Y P570Y QF@Yc@Y$'QY GI7 tS)Ec W &8YIPw `cxsh Z[ Example 1. [What do you think the [scatter plot of the list1[and list2 will be?[ Solutioin:[-By sellecting the SetGraph[from the menu, we tick['StatGraph1' and choose[XList andYlist to be list1[and list2 respectively [under the 'Setting'.[-Now the scatter plot[for SetGraph1 should[look like a cosine curve.[-Tap 'Calc' under the [menu bar, and select['Sinusoidal Reg', we get[a curve that is best [fitting the cosine curve.[[ Question: [The regression[equation does not look [like 'y=cos(x)', what is[it? [ Example 2. [What do you think the [scatter plot of the list1[and list3 will be?[ Solution:[-By sellecting the [SetGraph from the menu,[we tick 'StatGraph2' and[choose XList andYlist to[be list1 and list3 respectively[under the 'Setting'.[-Now the scatter plot[for SetGraph3 should[look like a 'Sine' curve.[-Tap 'Calc' under the [menu bar, and select['Sinusoidal Reg', we get[a curve that is best [fitting the cosine curve.[Remark: [The regression[equation now looks almost[identical to 'y=sin(x)'. [[ Exercise 1.[Use the existing list1, [list2 and list3 to create[a scatter plot for [list4 =list3/list2. What [do you the scatter plot[will be?[[Answer: The list4 is[already created together[with list2 and list3 in the[previous ListEditor. The[graph should look like ['y=tan(x)'. You might[need to adjust the View[Window to recognize[the graph to be [ 'y=tan(x)'.[[ Exercise 2.[Use the existing list1, [list2 and list3 to create[a scatter plot for [list4 =list2/list3. What [do you the scatter plot[will be?[The graph should look [like 'y=cot(x)'. ['y=tan(x)'. You might[need to adjust the View[Window to recognize[the graph to be [ 'y=cot(x)'.[[ **Radius 2[020 18.94736842 1.891634483 0.6493989384 37.89473684 1.578281019 1.228425425 56.84210526 1.093896316 1.674332957 75.78947369 0.4909709743 1.938800532 94.7368421 -0.1651586909 1.993168986 113.6842105 -0.8033908493 1.831546653 132.6315789 -1.354563143 1.471447821 151.5789474 -1.758947502 0.9518947861 170.5263158 -1.972722607 0.3291891806 189.4736842 -1.972722607 -0.3291891806 208.4210526 -1.758947502 -0.9518947861 227.3684211 -1.354563143 -1.471447821 246.3157895 -0.8033908493 -1.831546653 265.2631579 -0.1651586909 -1.993168986 284.2105263 0.4909709743 -1.938800532 303.1578947 1.093896316 -1.674332957 322.1052632 1.578281019 -1.228425425 341.0526316 1.891634483 -0.6493989384020\radius 2Graph2D| Graph3D LISTSYS4NModify $ STATCALC NSTATSYS \NSequenceX, Sheet| Sheet3D| SolveEq|SolveLwr SolveUpr StupFLG1(StupListD StupPict$ ViewWind( D P \ h t              ! 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