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Add basic reciprocal trig function exercise
Reviewers: emily, eater Reviewed By: eater CC: eater, emily Differential Revision: http://phabricator.khanacademy.org/D570
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<!DOCTYPE html> | |||
<html data-require="math math-format graphie"> | |||
<head> | |||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> | |||
<title>Reciprocal trig functions</title> | |||
<script src="../khan-exercise.js"></script> | |||
<script> | |||
function betterTriangle(width, height, A, B, C, a, b, c) { | |||
var scale = 5 / Math.sqrt(width * width + height * height); | |||
width *= scale; | |||
height *= scale; | |||
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with(KhanUtil.currentGraph) { | |||
// Leave some space for the labels | |||
init({range: [[-1.5, width + 1], [-1, height + 1]]}); | |||
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path([[0, 0], [width, 0], [0, height], true]); | |||
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label([0, height], A, "above left"); | |||
label([0, 0], C, "below left"); | |||
label([width, 0], B, "below right"); | |||
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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="problems"> | |||
<div id="csc"> | |||
<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> | |||
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<var id="HYPOTENUSE_NAME">"AB"</var> | |||
<var id="HYPOTENUSE_VALUE">AB</var> | |||
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<var id="SIMPLE_CSC">fraction(AB, OPPOSITE_VALUE)</var> | |||
<var id="SIMPLE_SIN">fraction(OPPOSITE_VALUE, AB)</var> | |||
<var id="CSC">AB / OPPOSITE_VALUE</var> | |||
</div> | |||
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<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>\csc(\angle <var>ANGLE</var>)?</code> | |||
</p> | |||
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<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> | |||
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<div class="solution" data-forms="proper, improper" data-simplify="optional"><var>CSC</var></div> | |||
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<div class="hints"> | |||
<p> | |||
<code>\csc(\angle <var>ANGLE</var>) = | |||
\dfrac{1}{\sin(\angle <var>ANGLE</var>)}</code> | |||
</p> | |||
<p> | |||
How can we find | |||
<code>\sin(\angle <var>ANGLE</var>)</code>? | |||
</p> | |||
<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> | |||
<p> | |||
<code>\csc(\angle <var>ANGLE</var>) | |||
= \dfrac{1}{\sin(\angle <var>ANGLE</var>)} | |||
= <var>SIMPLE_CSC</var></code> | |||
</p> | |||
</div> | |||
</div> | |||
<div id="sec"> | |||
<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> | |||
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<var id="HYPOTENUSE_NAME">"AB"</var> | |||
<var id="HYPOTENUSE_VALUE">AB</var> | |||
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<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; | |||
} | |||
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return AB; | |||
})() | |||
</var> | |||
<var id="SIMPLE_COS">fraction(ADJACENT_VALUE, AB)</var> | |||
<var id="SIMPLE_SEC">fraction(AB, ADJACENT_VALUE)</var> | |||
<var id="SEC">AB / ADJACENT_VALUE</var> | |||
</div> | |||
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<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>\sec(\angle <var>ANGLE</var>)?</code> | |||
</p> | |||
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<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> | |||
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<div class="solution" data-forms="proper, improper" data-simplify="optional"><var>SEC</var></div> | |||
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<div class="hints"> | |||
<p> | |||
<code>\sec(\angle <var>ANGLE</var>) = | |||
\dfrac{1}{\cos(\angle <var>ANGLE</var>)}</code> | |||
</p> | |||
<p> | |||
How can we find | |||
<code>\cos(\angle <var>ANGLE</var>)</code>? | |||
</p> | |||
<p> | |||
SOH <b>CAH</b> TOA | |||
</p> | |||
<p> | |||
<b>C</b>osine = <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> | |||
<p> | |||
<code>\sec(\angle <var>ANGLE</var>) | |||
= \dfrac{1}{\cos(\angle <var>ANGLE</var>)} | |||
= <var>SIMPLE_SEC</var></code> | |||
</p> | |||
</div> | |||
</div> | |||
<div id="cot"> | |||
<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> | |||
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<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; | |||
} | |||
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return AB; | |||
})() | |||
</var> | |||
<var id="SIMPLE_TAN">fraction(OPPOSITE_VALUE, ADJACENT_VALUE) | |||
</var> | |||
<var id="SIMPLE_COT">fraction(ADJACENT_VALUE, OPPOSITE_VALUE) | |||
</var> | |||
<var id="COT">ADJACENT_VALUE / OPPOSITE_VALUE</var> | |||
</div> | |||
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<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>\cot(\angle <var>ANGLE</var>)?</code> | |||
</p> | |||
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<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> | |||
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<div class="solution" data-forms="proper, improper" data-simplify="optional"><var>COT</var></div> | |||
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<div class="hints"> | |||
<p> | |||
<code>\cot(\angle <var>ANGLE</var>) = | |||
\dfrac{1}{\tan(\angle <var>ANGLE</var>)}</code> | |||
</p> | |||
<p> | |||
How can we find | |||
<code>\tan(\angle <var>ANGLE</var>)</code>? | |||
</p> | |||
<p> | |||
SOH CAH <b>TOA</b> | |||
</p> | |||
<p> | |||
<b>T</b>angent = <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> | |||
<p> | |||
<code>\cot(\angle <var>ANGLE</var>) | |||
= \dfrac{1}{\tan(\angle <var>ANGLE</var>)} | |||
= <var>SIMPLE_COT</var></code> | |||
</p> | |||
</div> | |||
</div> | |||
</div> | |||
</div> | |||
</body> | |||
</html> |
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@@ -401,3 +401,4 @@ $.extend(KhanUtil, { | ||
} | } | ||
} | } | ||
}); | }); | ||
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