TR5 Checkit

source/precalculus/exercises/bank.xml

@@ -355,7 +355,7 @@
             <description>
                Find exact values of trigonometric functions of special angles (30, 45, and 60). 
             </description>
-        </outcome>
+        </outcome> -->
 
         <outcome>
             <title>The Unit Circle</title>
@@ -366,7 +366,7 @@
             </description>
         </outcome>
 
-        <outcome>
+        <!-- <outcome>
             <title>Properties of Sine and Cosine Graphs</title>
             <slug>PF1</slug>
             <path>outcomes/PF/PF1</path>

source/precalculus/exercises/outcomes/TR/TR5/generator.sage

@@ -0,0 +1,45 @@
+load("../../../source/common/sagemath/library.sage")
+class Generator(BaseGenerator):
+    triples = sorted(TBIL.pythagorean_triples(max_length=50))
+    def data(self):
+
+        functions=sample([sin,cos,tan,sec,csc,cot],5)
+        angles=sample([i*pi/6 for i in [1..11]]+[(2*i+1)*pi/4 for i in [0..3]],3)
+        triple=choice(Generator.triples)
+        quadrant=choice(["I","II","III","IV"])
+        if quadrant=="I" or quadrant=="IV":
+            angles.append(arctan(triple[1]/triple[0]))
+        else:
+            angles.append(pi+arctan(triple[1]/triple[0]))
+        degrees=[True,False]
+        shuffle(degrees)
+
+        angle_strings= [ f"{latex(s*360/(2*pi))}"+r"^\circ" if degrees[i] else TBIL.typeset_angle(s) for i,s in enumerate(angles[:2])]
+        values=[functions[0](angles[0]),functions[1](angles[1]),functions[2](angles[2]),functions[3](angles[2]),functions[4](angles[3])]
+        for (i,v) in enumerate(values):
+            if v.is_infinity():
+                values[i]=r"\text{undefined}"
+        coordinate, coordinate_value =choice([("x",cos(angles[3])),("y",sin(angles[3]))])
+
+
+
+        return {
+            "task1": [ {"angle": angle_strings[i], "value": values[i], "f":functions[i].name()} for i in [0,1]],
+            "angle2": angles[2],
+            "point2": (cos(angles[2]),sin(angles[2])),
+            "task2": [ {"value": values[i], "f":functions[i].name()} for i in [2,3]], 
+            "angle3": angles[3],
+            "quadrant3": quadrant,
+            "coordinate3": coordinate,
+            "coordinate3_value": simplify(coordinate_value),
+            "f3": functions[4].name(),
+            "value3": simplify(values[4])
+        }
+
+    @provide_data
+    def graphics(data):
+        p=TBIL.plot_angle(data["angle2"],label_unit_point=True,show_angle_value=r"$\theta$",show_unit_circle=True)
+        q=TBIL.plot_angle(data["angle3"],label_unit_point=("x","y"),show_angle_value=r"$\alpha$",show_unit_circle=True)
+
+        return {"plot2": p, "plot3": q
+               }

source/precalculus/exercises/outcomes/TR/TR5/template.xml

@@ -0,0 +1,65 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
+    <knowl>
+        <intro>
+            <p>
+            Compute an exact value (not a decimal approximation) for each of the following.
+            </p>
+        </intro>
+        <!--{{#task1}}-->
+        <knowl>
+            <content>
+                <p><m>\{{f}}\left({{angle}}\right)</m>.</p>
+            </content>
+            <outtro>
+                <p><m>\{{f}}\left({{angle}}\right)={{value}}</m>
+                </p>
+            </outtro>
+        </knowl>
+        <!--{{/task1}}-->
+    </knowl>
+    <knowl>
+        <intro>
+            <p>Let <m>\theta</m> be an angle drawn in standard position that intersects the unit circle at
+                 <m>{{point2}}</m>.
+            </p>
+            <p>
+                <image
+                source="assets/TR5/generated/{{__seed__}}/plot2.png"
+                description="."
+                width="50%"/>
+            </p>
+            <p>
+            Compute an exact value (not a decimal approximation) for each of the following.
+            </p>
+        </intro>
+        <!--{{#task2}}-->
+        <knowl>
+            <content>
+                <p><m>\{{f}}(\theta)</m>.</p>
+            </content>
+            <outtro>
+                <p><m>\{{f}}(\theta)={{value}}</m>
+                </p>
+            </outtro>
+        </knowl>
+        <!--{{/task2}}-->
+    </knowl>
+    <knowl>
+        <content>
+            <p>Let <m>(x,y)</m> be a point on the unit circle that lies in Quadrant {{quadrant3}} with 
+            an <m>{{coordinate3}}</m>-value of <m>{{coordinate3_value}}</m>.  Let <m>\alpha</m> be the angle 
+            in standard position that intersects the unit circle at this point.</p> 
+            <p>
+                <image
+                source="assets/TR5/generated/{{__seed__}}/plot3.png"
+                description="."
+                width="50%"/>
+            </p>
+            <p>Compute <m>\{{f3}}(\alpha)</m>.</p>
+        </content>
+        <outtro>
+            <p><m>\{{f3}}(\alpha)={{value3}}</m></p>
+        </outtro>
+    </knowl>
+</knowl>