Skip to content
This repository has been archived by the owner on May 11, 2021. It is now read-only.

Commit

Permalink
Trig identity exercise
Browse files Browse the repository at this point in the history
  • Loading branch information
@igorT
igorT committed Jul 22, 2011
1 parent fb9c771 commit acc0089
Show file tree
Hide file tree
Showing 2 changed files with 276 additions and 0 deletions.
57 changes: 57 additions & 0 deletions exercises/trig_identities_1.html
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,57 @@
<!DOCTYPE html>
<html data-require="math math-format convert-values">
<head>
<title>Trigonometry identities 1</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="START_TYPE">trigTypes[randRange(0,trigTypes.length-1)]</var>

<var id="END_TYPE" data-ensure="START_TYPE !== END_TYPE && !((START_TYPE.name === 'sin' || START_TYPE.name === 'cos') && END_TYPE.name === 'tan' ) ">trigTypes[randRange(0,trigTypes.length-1)]</var>
<var id="END_NAME">END_TYPE.name</var>
<var id="FUN_NAME">START_TYPE.name</var>
<var id="ANGLE">function(){
if ( START_TYPE.name === "tan" ){
return randFromArray([0,30,45,60]);
}
else if ( START_TYPE.name === "sec" ){
return randFromArray([0,30,45,60]);
}
else if (START_TYPE.name === "csc" ){
return randFromArray([30,45,60,90]);
}
else{
return randFromArray([0,30,45,60,90]);
}}()

</var>
<var id="FUN_VALUE">START_TYPE.print( ANGLE )</var>
<var id="SOLUTION">END_TYPE.print( ANGLE )</var>
<var id="STEPS">findSteps(START_TYPE , END_TYPE, ANGLE)</var>

<var id="WRONG_ANGLE1" data-ensure="ANGLE !== WRONG_ANGLE1"> randFromArray([0,30,45,60,90])</var>
<var id="WRONG_ANGLE2" data-ensure="ANGLE !== WRONG_ANGLE2 && WRONG_ANGLE2 !== WRONG_ANGLE1"> randFromArray([0,30,45,60,90])</var>
<var id="NUM_ANSWERS">["","","","","","","","","","","",""]</var>

</div>

<div class="problems">
<div>
<p class="question">Given that x is in first quadrant and <code> \<var>FUN_NAME</var> x </code> is <code><var>FUN_VALUE</var></code> what is <code> \<var>END_NAME</var> x</code> ?</p>


<p class="solution"><code><var>SOLUTION</var></code></p>
<ul class="choices" data-show="4" data-none="true">
<li data-each="NUM_ANSWERS"><code><var>trigTypes[randRange(0,trigTypes.length-1)].print( randFromArray([0,30,45,60,90]) )</var></code></li>
</ul>
</div>
</div>

<div class="hints">
<div data-each="STEPS as step"><p data-each="step as value"><code><var>value</var></code></p><hr></div>
</div>
</div>
</body>
</html>
219 changes: 219 additions & 0 deletions utils/convert-values.js
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,219 @@
jQuery.extend( KhanUtil, {
trigFunc: {
csc: {name: "csc", print: function( angle ){
return KhanUtil.trigFunc.sec.print( 90-angle);
},
convertsTo:["sin"],
convertTo: function( type, angle ){
if( type.name == "sin" ){
var cscv = KhanUtil.trigFunc.csc.print( angle );
var sinv = KhanUtil.trigFunc.sin.print( angle );
toReturn = new Array();
toReturn.push( "\\csc x = \\frac{1}{\\sin x}" );
toReturn.push( "\\csc x = " + cscv );
toReturn.push( '\\frac{1}{\\sin x} = ' + cscv );
toReturn.push( '\\sin x = ' + sinv );
return toReturn;
}

}
},
sec: {name: "sec", print: function( angle ){
if( angle == 0 ){
return 1;
}
else if( angle == 30 ){
return "\\frac{2}{\\sqrt 3}";
}
else if( angle == 45 ){
return '\\sqrt 2';
}
else if( angle == 60 ){
return '2';
}
else if( angle == 90 ){
return 'undefined';
}
return 'undef';
},
convertsTo: ["cos","tan"],
convertTo: function( type, angle){
if( type.name == "cos" ){
var cosv = KhanUtil.trigFunc.cos.print( angle );
var secv = KhanUtil.trigFunc.sec.print( angle );
toReturn = new Array();
toReturn.push( "\\sec x = \\frac{1}{\\cos x}" );
toReturn.push( "\\sec x = " + secv );
toReturn.push( '\\frac{1}{\\cos x} = ' + secv );
toReturn.push( "\\cos x = " + cosv);
return toReturn;
}
else if( type.name == "tan"){
var tanv = KhanUtil.trigFunc.tan.print( angle );
var secv = KhanUtil.trigFunc.sec.print( angle );
toReturn = new Array();
toReturn.push( "\\sin^2 x + \\cos^2 x = 1" );
toReturn.push( "\\frac{\\sin^2 x}{\\cos^2 x} + \\frac{\\cos^2 x}{\\cos^2 x} = \\frac{1}{\\cos^2 x}" );
toReturn.push( "\\tan^2 x + 1 = \\sec^2 x" );
toReturn.push( "\\tan^2 x + 1 = (" + secv + ")^2" );
toReturn.push( "\\tan^2 x = (" + secv + ")^2 - 1" );
toReturn.push( "\\tan x = \\sqrt { " + secv + " ^2 - 1 }");
toReturn.push( "\\tan x = " + tanv );
return toReturn;
}
}
},
tan: {name: "tan", print: function( angle ){
if( angle == 0 ){
return 0;
}
else if( angle == 30 ){
return "\\frac{1}{\\sqrt 3}";
}
else if( angle == 45 ){
return '1';
}
else if( angle == 60 ){
return '\\sqrt 3';
}
else if( angle == 90 ){
return 'undefined';
}
return 'undef';

},
convertsTo: ["sec"],
convertTo: function( type, angle){
if( type.name == "sec" ){

var tanv = KhanUtil.trigFunc.tan.print( angle );
var secv = KhanUtil.trigFunc.sec.print( angle );
toReturn = new Array();
toReturn.push( "\\sin^2 x + \\cos^2 x = 1" );
toReturn.push( "\\frac{\\sin^2 x}{\\cos^2 x} + \\frac{\\cos^2 x}{\\cos^2 x} = \\frac{1}{\\cos^2 x}" );
toReturn.push( "\\tan^2 x + 1 = \\sec^2 x" );
toReturn.push( "(" + tanv + ")^2 + 1 = \\sec^2 x" );
toReturn.push( "\\sqrt{(" + tanv + ")^2 + 1} = \\sec x" );
toReturn.push( secv + ' = \\sec x');
return toReturn;
}
}
},
cos :{name: "cos", print: function( angle ){
return KhanUtil.trigFunc.sin.print( 90-angle );
},
convertsTo: ["sin","sec"],
convertTo: function( type, angle){
if( type.name == "sin" ){
var cosv = KhanUtil.trigFunc.cos.print( angle );
var sinv = KhanUtil.trigFunc.sin.print( angle );
toReturn = new Array();
toReturn.push("\\sin^2 x + \\cos^2 x = 1");
toReturn.push("\\sin^2 x + (" + cosv + ")^2 = 1");
toReturn.push("(" + cosv + ")^2 = 1 - \\sin^2 x");
toReturn.push('(' + cosv + ')^2 - 1 = - \\sin^2 x');
toReturn.push('-(' + cosv + ')^2 + 1 = \\sin^2 x');
toReturn.push(sinv + ' = \\sin x');
return toReturn;
}
else if( type.name == "sec" ){
cosv = KhanUtil.trigFunc.cos.print( angle );
secv = KhanUtil.trigFunc.sec.print( angle );
toReturn = new Array();
toReturn.push( cosv + " = \\cos x" );
toReturn.push( secv + " = \\frac{1}{\\cos x}" );
toReturn.push( secv + " = \\sec x" );
return toReturn;
}
}
},
sin: {name: "sin", print: function( angle ){
if( angle == 0 ){
return 0;
}
else if( angle == 30 ){
return '\\frac{1}{2}';
}
else if( angle == 45 ){
return '\\frac{\\sqrt 2}{2}';
}
else if( angle == 60 ){
return '\\frac{\\sqrt 3}{2}';
}
else if( angle == 90 ){
return '1';
}
return 'undefined';
},
convertsTo: ["cos","csc"],
convertTo: function( type, angle ){
if( type.name == "cos" ){
var sinv = KhanUtil.trigFunc.sin.print( angle );
var cosv = KhanUtil.trigFunc.cos.print( angle );
toReturn = new Array();
toReturn.push( "\\sin^2 x + \\cos^2 x = 1" );
toReturn.push( "(" + sinv + ")^2 + \\cos^2 x = 1" );
toReturn.push( "(" + sinv + ")^2 = 1- \\cos^2 x " );
toReturn.push( "(" + sinv + ")^2 - 1 = - \\cos^2 x " );
toReturn.push( "-(" + sinv + ")^2 + 1 = \\cos^2 x " );
toReturn.push( cosv + " = \\cos x" );
return toReturn;

}
else if( type.name == "csc" ){
var sinv = KhanUtil.trigFunc.sin.print( angle )
var cscv = KhanUtil.trigFunc.csc.print( angle );

toReturn = new Array();
toReturn.push( sinv + " = \\sin x" );
toReturn.push( cscv + " = \\frac{1}{\\sin x}" );
toReturn.push( cscv + " = \\csc x" );
return toReturn;
}
}

}
}})

jQuery.extend( KhanUtil, {
trigTypes: [KhanUtil.trigFunc.sin,KhanUtil.trigFunc.cos,KhanUtil.trigFunc.tan,KhanUtil.trigFunc.csc,KhanUtil.trigFunc.sec],

findSteps: function( start, end, value){
var visited = {};
var queue=[];
var next=start;
while( next.name != end.name ){
if ( next.convertsTo ) {
$.each( next.convertsTo, function(i, str) {
if( ! (str in visited) ){
var move = KhanUtil.trigFunc[str];
move["parent"] = next;
queue.push( move );
}
visited[str] = true;
});
}
next = queue.shift();
}
var prev = next;
var steps = new Array();
while( prev.name != start.name ){
steps.unshift( prev.name );
prev = prev.parent;

}
steps.unshift( prev.name );
var toReturn = new Array();
for( x=0; x<steps.length-1 ;x++ ){
// Vars cannot have circular references, so delete .parent before returning
var step = KhanUtil.trigFunc[steps[x]].convertTo( KhanUtil.trigFunc[steps[x+1]], value );
delete step.parent;

toReturn.push( step );
}
for( x=0; x<KhanUtil.trigTypes.length-1 ;x++ ){
delete KhanUtil.trigTypes[x].parent;
}
return toReturn;
}
})

0 comments on commit acc0089

Please sign in to comment.