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<!DOCTYPE html>
<!-- TODO: Improve hints -->
<html data-require="math graphie math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Trigonometry 0.5</title>
<script src="../khan-exercise.js"></script>
<script>
function fractionSQRoot(b, root){
var natRoot = KhanUtil.splitRadical( root )[0];
var underRoot = KhanUtil.splitRadical( root )[1];
var d = KhanUtil.reduce( natRoot * underRoot, b )[0];
var n = KhanUtil.reduce( natRoot * underRoot, b )[1];
if ( d === 1 ){
if ( n !== 1 ) {
return n + "\\sqrt{" + underRoot +"}";
}
else{
return "\\sqrt{" + underRoot + "}";
}
}
else if ( underRoot !== 1 ) {
if ( n !== 1 ) {
return "\\dfrac{" + n + "\\sqrt{" + underRoot +"} }{"+ d + "}";
}
else {
return "\\dfrac{ \\sqrt{" + underRoot + "}}{" + d + "}";
}
}
else {
return "\\dfrac{" + n + "}{" + d + "}";
}
}
function betterTriangle(width, height, A, B, C, a, b, c) {
var scale = 5 / Math.sqrt(width * width + height * height);
width *= scale;
height *= scale;
with ( KhanUtil.currentGraph ) {
// Leave some space for the labels
init({ range: [[-1.5, width + 1], [-1, height + 1]] });
path([ [0, 0], [width, 0], [0, height], true ]);
label( [0, height], A, "above left" );
label( [0, 0], C, "below left" );
label( [width, 0], B, "below right" );
label( [0, height/2], b, "left" );
label( [width/2, 0], a, "below" );
label( [width/2, height/2], c, "above right", {
labelDistance: 3
} );
}
}
</script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="AC, BC">shuffle(randFromArray([[3,4], [6,8], [5,12], [7, 24], [8, 15], [10, 24], [12,16]]))</var>
<var id="CB">BC</var>
<var id="AB">sqrt(AC * AC + BC * BC)</var>
<var id="ANGLE">randFromArray([
"ABC",
"BAC"
])</var>
<var id="OPPOSITE_NAME">(ANGLE.substring(0,1) + ANGLE.substring(2))</var>
<var id="OPPOSITE_VALUE">
(function(){
if ( OPPOSITE_NAME === "AC" ){
return AC;
}
else if ( OPPOSITE_NAME === "BC" ){
return CB;
}
return AB;
})()
</var>
<var id="HYPOTENUSE_NAME">"AB"</var>
<var id="HYPOTENUSE_VALUE">AB</var>
<var id="ADJACENT_NAME">ANGLE.substring(1)</var>
<var id="ADJACENT_VALUE">
(function(){
if ( ADJACENT_NAME === "AC" ){
return AC;
}
else if ( ADJACENT_NAME === "BC" ){
return BC;
}
return AB;
})()
</var>
<var id="SIMPLE_TAN">fraction( OPPOSITE_VALUE, ADJACENT_VALUE, false, false, false, false)</var>
<var id="TAN">OPPOSITE_VALUE / ADJACENT_VALUE</var>
<var id="SIMPLE_SIN">fraction(OPPOSITE_VALUE, AB)</var>
<var id="SIN">OPPOSITE_VALUE / AB</var>
<var id="SIMPLE_COS">fraction(ADJACENT_VALUE, AB)</var>
<var id="COS">ADJACENT_VALUE / AB</var>
</div>
<div class="problems">
<div id="sinTrig1">
<div class="problem">
<p><code>\overline{AC}</code> is <code><var>AC</var></code> units long</p>
<p><code>\overline{BC}</code> is <code><var>BC</var></code> units long</p>
<p><code>\overline{AB}</code> is <code><var>AB</var></code> units long</p>
</div>
<div class="question">
<p>What is <code>\sin(\angle <var>ANGLE</var>)</code> ?</p>
<div class="graphie">
betterTriangle( BC, AC, "A", "B", "C", BC, AC, AB );
path([ [ 0.4, 0 ], [ 0.4, 0.4 ], [ 0, 0.4 ] ]);
</div>
</div>
<div class="solution" data-type="rational" data-simplify="optional"><var>SIN</var></div>
<div class="hints">
<p><b>SOH</b> CAH TOA</p>
<p><b>S</b>in = <b>O</b>pposite over <b>H</b>ypotenuse</p>
<p>opposite <code>= \overline{<var>OPPOSITE_NAME</var>} = <var>OPPOSITE_VALUE</var></code></p>
<p>hypotenuse <code>= \overline{<var>HYPOTENUSE_NAME</var>} = <var>AB</var></code></p>
<p><code>\sin(\angle <var>ANGLE</var>)=<var>SIMPLE_SIN</var></code></p>
</div>
</div>
<div id="cosTrig1" data-type="sinTrig1">
<div class="problem">
<p><code>\overline{AC}</code> is <code><var>AC</var></code> units long</p>
<p><code>\overline{BC}</code> is <code><var>BC</var></code> units long</p>
<p><code>\overline{AB}</code> is <code><var>AB</var></code> units long</p>
</div>
<div class="question">
<p>What is <code>\cos(\angle <var>ANGLE</var>)</code> ?</p>
<div class="graphie">
betterTriangle( BC, AC, "A", "B", "C", BC, AC, AB );
path([ [ 0.4, 0 ], [ 0.4, 0.4 ], [ 0, 0.4 ] ]);
</div>
</div>
<div class="solution" data-type="rational" data-simplify="optional"><var>COS</var></div>
<div class="hints">
<p>SOH <b>CAH</b> TOA</p>
<p><b>C</b>os = <b>A</b>djacent over <b>H</b>ypotenuse</p>
<p>adjacent <code>= \overline{<var>ADJACENT_NAME</var>} = <var>ADJACENT_VALUE</var></code></p>
<p>hypotenuse <code>= \overline{<var>HYPOTENUSE_NAME</var>} = <var>AB</var></code></p>
<p><code>\cos(\angle <var>ANGLE</var> )=<var>SIMPLE_COS</var></code></p>
</div>
</div>
<div id="tanTrig1" data-type="sinTrig1">
<div class="problem">
<p><code>\overline{AC}</code> is <code><var>AC</var></code> units long</p>
<p><code>\overline{BC}</code> is <code><var>BC</var></code> units long</p>
<p><code>\overline{AB}</code> is <code><var>AB</var></code> units long</p>
</div>
<div class="question">
<p>What is <code>\tan(\angle <var>ANGLE</var>)</code> ?</p>
<div class="graphie">
betterTriangle( BC, AC, "A", "B", "C", BC, AC, AB );
path([ [ 0.4, 0 ], [ 0.4, 0.4 ], [ 0, 0.4 ] ]);
</div>
</div>
<div class="solution" data-type="rational" data-simplify="optional"><var>TAN</var></div>
<div class="hints">
<p>SOH CAH <b>TOA</b></p>
<p><b>T</b>an = <b>O</b>pposite over <b>A</b>djacent</p>
<p>opposite <code>= \overline{<var>OPPOSITE_NAME</var>} = <var>OPPOSITE_VALUE</var></code></p>
<p>adjacent <code>= \overline{<var>ADJACENT_NAME</var>} = <var>ADJACENT_VALUE</var></code></p>
<p><code>\tan(\angle <var>ANGLE</var>)=<var>SIMPLE_TAN</var></code></p>
</div>
</div>
</div>
</div>
</body>
</html>
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