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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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