qu.1.topic=Trigonometric Functions@

qu.1.1.mode=Inline@
qu.1.1.name=Radian to Degree@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=switch(rint(17),"0","Pi/6","Pi/4","Pi/3","Pi/2","2*Pi/3","3*Pi/4",
"5*Pi/6","Pi","7*Pi/6","5*Pi/4","4*Pi/3","3*Pi/2","5*Pi/3","7*Pi/4",
"11*Pi/6","2*Pi");
$n=rint(2);
$b="(-1)^($n)*($a)";
$dispb=maple("printf(MathML[ExportPresentation]($b))");
$ANS=$b*180/Pi;@
qu.1.1.uid=437932b4-1324-42d4-bca4-a20d43d3ee1c@
qu.1.1.weighting=1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.maple_answer=$ANS@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.libname=@
qu.1.1.part.1.mode=Maple@
qu.1.1.part.1.allow2d=1@
qu.1.1.part.1.plot=@
qu.1.1.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.1.type=formula@
qu.1.1.question=<p>Convert the radian measure $dispb to degrees. (Omit the degree symbol in your answer.)</p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.2.mode=Inline@
qu.1.2.name=Exact Trig@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$trig=[4,3,6];
$picktrig=switch(rint(3),$trig);
$picktrig2=switch(rint(3),$trig);
condition: ne($picktrig,$picktrig2);
$ANS1="sin(Pi/$picktrig)";
$ANS2="tan(Pi/$picktrig2)";@
qu.1.2.uid=a40bb69d-8397-4741-a769-2017288ad35e@
qu.1.2.weighting=1,1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.name=sro_id_1@
qu.1.2.part.1.maple_answer=$ANS1@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.question=(Unset)@
qu.1.2.part.1.libname=@
qu.1.2.part.1.mode=Maple@
qu.1.2.part.1.allow2d=1@
qu.1.2.part.1.plot=@
qu.1.2.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.1.type=formula@
qu.1.2.part.2.name=sro_id_2@
qu.1.2.part.2.maple_answer=$ANS2@
qu.1.2.part.2.editing=useHTML@
qu.1.2.part.2.question=(Unset)@
qu.1.2.part.2.libname=@
qu.1.2.part.2.mode=Maple@
qu.1.2.part.2.allow2d=1@
qu.1.2.part.2.plot=@
qu.1.2.part.2.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.2.type=formula@
qu.1.2.question=<p>Using special triangles, determine the following:</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mi>&pi;</mi><mrow><mi>$picktrig</mi></mrow></mfrac></mrow></mfenced></mrow></mstyle></math>&nbsp;&nbsp; <span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>tan</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mi>&pi;</mi><mrow><mi>$picktrig2</mi></mrow></mfrac></mrow></mfenced></mrow></mstyle></math>&nbsp; <span>&nbsp;</span><2><span>&nbsp;</span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=Function Describing Model@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$p=[6,8,10,12,14];
$rp=switch(rint(5),$p);
$max=[120,140,160,180];
$ymax=switch(rint(4),$max);
$min=[40,60,80];
$ymin=switch(rint(3),$min);
$m="2*Pi/$rp";
$dispm=maple("MathML[ExportPresentation]($m)");
$K=($ymax-$ymin)/2;
$b=($ymax+$ymin)/2;
$ANS="$K*sin($m*t)+$b";@
qu.1.3.uid=d4bfc802-380c-4332-a6f7-106c85c2dd92@
qu.1.3.weighting=1@
qu.1.3.numbering=alpha@
qu.1.3.part.1.name=sro_id_1@
qu.1.3.part.1.maple_answer=$ANS@
qu.1.3.part.1.editing=useHTML@
qu.1.3.part.1.question=(Unset)@
qu.1.3.part.1.libname=@
qu.1.3.part.1.mode=Maple@
qu.1.3.part.1.allow2d=1@
qu.1.3.part.1.plot=@
qu.1.3.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.3.part.1.type=formula@
qu.1.3.question=<p><font size="3">A quantity varies sinusoidally by <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>Ksin</mi><mfenced open='(' close=')' separators=','><mrow><mi>m</mi><mfenced open='(' close=')' separators=','><mrow><mi>t</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfenced></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>b</mi></mrow></mstyle></math> where <em>K, m, a,</em> and <em>b</em> are constants.&nbsp; If the quantity has a period of $rp days, a maximum value of $ymax and a minimum value of $ymin, what is the function that models this quantity?</font></p><p><font size="3">Hint:&nbsp;Enter 'Pi' </font><font size="3">to represent <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&pi;</mi></mrow></mstyle></math>.</font></p><p><span>&nbsp;y = </span><1><span>&nbsp;</span></p>@

qu.1.4.mode=Inline@
qu.1.4.name=Trig Identities ii@
qu.1.4.comment=@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$func1=switch(rint(2),"sin(x)","cos(x)");
$func2=switch(rint(2),"tan(x)","csc(x)");
$func3=switch(rint(2),"sec(x)","cot(x)");
$func4=switch(rint(6),"sin(x)","cos(x)","tan(x)","sec(x)","cot(x)","csc(x)");
condition: ne($func1,$func4) ne($func2,$func4) ne($func3,$func4);
$func="($func1)*($func2)*($func3)*($func4)";
$disp=maple("MathML[ExportPresentation]($func)");@
qu.1.4.uid=b6f143be-104a-497c-a837-e7b2cfd31e50@
qu.1.4.weighting=1@
qu.1.4.numbering=alpha@
qu.1.4.part.1.name=sro_id_1@
qu.1.4.part.1.maple_answer=simplify($func)@
qu.1.4.part.1.editing=useHTML@
qu.1.4.part.1.question=(Unset)@
qu.1.4.part.1.libname=@
qu.1.4.part.1.mode=Maple@
qu.1.4.part.1.allow2d=1@
qu.1.4.part.1.plot=@
qu.1.4.part.1.maple=evalb(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.1.type=formula@
qu.1.4.question=<p>Using trig identities simplfy the following:</p><p>$disp</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.5.mode=Inline@
qu.1.5.name=Trig Identities@
qu.1.5.comment=@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=rint(2,6);
$func=switch(rint(3),"$a*sin(x)^2+$a*cos(x)^2","$a*sec(x)^2-$a*tan(x)^2","$a*csc(x)^2-$a*cot(x)^2");
$disp=maple("printf(MathML[ExportPresentation]($func))");
$ANS=$a;@
qu.1.5.uid=831c7905-20fc-4297-acce-0569dba3c38a@
qu.1.5.weighting=1@
qu.1.5.numbering=alpha@
qu.1.5.part.1.name=sro_id_1@
qu.1.5.part.1.maple_answer=$ANS@
qu.1.5.part.1.editing=useHTML@
qu.1.5.part.1.question=(Unset)@
qu.1.5.part.1.libname=@
qu.1.5.part.1.mode=Maple@
qu.1.5.part.1.allow2d=1@
qu.1.5.part.1.plot=@
qu.1.5.part.1.maple=evalb(($ANSWER)-($RESPONSE) = 0);@
qu.1.5.part.1.type=formula@
qu.1.5.question=<p>Simplfy the following using trig identities: $disp</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.6.mode=Inline@
qu.1.6.name=Basic Period@
qu.1.6.comment=@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$a=rint(2,6);
$b=rint(2,9);
$c=rint(5,15);
$func="$a*sin($b*pi*x)+$c";
$disp=maple("MathML[ExportPresentation]($func)");
$ANS="2*pi/($b*pi)";@
qu.1.6.uid=61bdd425-b5af-40ef-ab05-0c6d2ee24718@
qu.1.6.weighting=1@
qu.1.6.numbering=alpha@
qu.1.6.part.1.name=sro_id_1@
qu.1.6.part.1.maple_answer=$ANS@
qu.1.6.part.1.editing=useHTML@
qu.1.6.part.1.question=(Unset)@
qu.1.6.part.1.libname=@
qu.1.6.part.1.mode=Maple@
qu.1.6.part.1.allow2d=1@
qu.1.6.part.1.plot=@
qu.1.6.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.6.part.1.type=formula@
qu.1.6.question=<p>The basic period of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$disp is</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.7.mode=Inline@
qu.1.7.name=Composite Functions (Trig)@
qu.1.7.comment=@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=$func1=switch(rint(2),"sin(x)","cos(x)");
$rfunc1="x->$func1";
$a=rint(2,10);
$func2=switch(rint(4),"x^2+x","x^3+$a","$a*x^2+11","x^3+x^2+x");
$rfunc2="x->$func2";
$m = maple("
MathML[ExportPresentation]($func1),
MathML[ExportPresentation]($func2),
convert(($rfunc1)(($rfunc2)(x)),string)
");
$disp1=switch(0,$m);
$disp2=switch(1,$m);
$ANS=switch(2,$m);@
qu.1.7.uid=7db77ea5-b429-42b8-8d2f-6bfdd29f1a91@
qu.1.7.weighting=1@
qu.1.7.numbering=alpha@
qu.1.7.part.1.name=sro_id_1@
qu.1.7.part.1.maple_answer=$ANS@
qu.1.7.part.1.editing=useHTML@
qu.1.7.part.1.question=(Unset)@
qu.1.7.part.1.libname=@
qu.1.7.part.1.mode=Maple@
qu.1.7.part.1.allow2d=1@
qu.1.7.part.1.plot=@
qu.1.7.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.7.part.1.type=formula@
qu.1.7.question=<p>Let <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$disp1 and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>g</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$disp2 then what is <span><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>f</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.1666667em' rspace='0.1666667em'>&compfn;</mo><mi>g</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math>?</span></p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.8.mode=Inline@
qu.1.8.name=Degrees to Radians@
qu.1.8.comment=@
qu.1.8.editing=useHTML@
qu.1.8.solution=@
qu.1.8.algorithm=$a=rint(1,360,13);
$n=rint(2);
$b=(-1)^($n)*($a);
$ANS=$b*Pi/180;@
qu.1.8.uid=1e4507cb-dc19-4ac6-ae5d-d98f0fdf29af@
qu.1.8.info=  Author=Steve Crane, Gord Clement;
  Sub-Topic=Radian Measure;
  Topic=Trig Functions;
  Course=Introductory Calculus for the Biological Sciences;
@
qu.1.8.weighting=1@
qu.1.8.numbering=alpha@
qu.1.8.part.1.name=sro_id_1@
qu.1.8.part.1.maple_answer=$ANS@
qu.1.8.part.1.editing=useHTML@
qu.1.8.part.1.question=(Unset)@
qu.1.8.part.1.libname=@
qu.1.8.part.1.mode=Maple@
qu.1.8.part.1.allow2d=1@
qu.1.8.part.1.plot=@
qu.1.8.part.1.maple=is(($ANSWER)-($RESPONSE) < 0.05);@
qu.1.8.part.1.type=formula@
qu.1.8.question=<p>Convert $b<sup>0</sup> to radian measure.</p><p>Give your answer to at least two decimal places.</p><p>Remember to enter 'Pi' for &pi;.</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

