TE5 Checkit

source/precalculus/exercises/bank.xml

@@ -429,7 +429,6 @@
                Use trigonometric functions and the Pythagorean Theorem to solve right triangles.
             </description>
         </outcome>
-      <!--
         <outcome>
             <title>Trigonometric Laws</title>
             <slug>TE5</slug>
@@ -438,7 +437,7 @@
                Use the law of sines and/or the law of cosines to solve non-right triangles.
             </description>
         </outcome>
-
+<!--
         <outcome>
             <title>Applications of Trigonometry</title>
             <slug>TE6</slug>

source/precalculus/exercises/outcomes/TE/TE5/generator.sage

@@ -0,0 +1,133 @@
+load("../../../source/common/sagemath/library.sage")
+class Generator(BaseGenerator):
+    def data(self):
+
+        tasks=[]
+
+        #Law of cosines
+        if choice([True,False]):
+            #SSS
+            sides = sample([5..15],2)
+            sides.append(choice([abs(sides[1]-sides[0])+1,sides[0]+sides[1]-1]))
+            shuffle(sides)
+            a,b,c=sides
+            C=round(arccos((a^2+b^2-c^2)/(2*a*b))*180/pi,1)
+            B=round(arccos((a^2+c^2-b^2)/(2*a*c))*180/pi,1)
+            A=round(arccos((b^2+c^2-a^2)/(2*b*c))*180/pi,1)
+            given=[f"a={latex(a)}",f"b={latex(b)}",f"c={latex(c)}"]
+            found=[f"A={latex(A)}^\\circ",f"B={latex(B)}^\\circ",f"C={latex(C)}^\\circ"]
+        else:
+            #SAS
+            sides = sample([5..15],2)
+            sides.sort()
+            angle=choice([10,15,..,80])*pi/180
+            sides.append(sqrt(sides[0]^2+sides[1]^2-2*sides[0]*sides[1]*cos(angle)))
+            angles = [ round(arcsin(sides[0]*sin(angle)/sides[2])*180/pi,1) ]
+            angles.append(round(180-angles[0]-angle*180/pi,1))
+            angles.append(angle*180/pi)
+
+            labels=[("a","A"),("b","B"),("c","C")]
+            shuffle(labels)
+            given = [f"{labels[0][0]}={sides[0]}",
+                     f"{labels[1][0]}={sides[1]}",
+                     f"{labels[2][1]}={angles[2]}^\\circ"]
+            found = [f"{labels[0][1]}={angles[0]}^\\circ",
+                     f"{labels[1][1]}={angles[1]}^\\circ",
+                     f"{labels[2][0]}={round(sides[2],1)}"]
+            shuffle(given)
+
+        tasks.append({"given": ",".join(given[:-1])+r",\text{ and }"+given[-1], 
+                      "found": ",".join(found[:-1])+r",\text{ and }"+found[-1],
+                    })
+
+        #Law of sines
+        angles=[a*pi/180 for a in sample([10,15,..,80],2)]
+        angles.append(pi-angles[0]-angles[1])
+        sides=[choice([5..15])]
+        sides.extend([round(sides[0]/sin(angles[0])*sin(angles[i]),1) for i in [1,2]])
+        labels=[("a","A"),("b","B"),("c","C")]
+        shuffle(labels)
+        if choice([True,False]):
+            #AAS
+            given = [f"{labels[0][1]}={angles[0]*180/pi}^\\circ",
+                     f"{labels[1][1]}={angles[1]*180/pi}^\\circ",
+                     f"{labels[0][0]}={sides[0]}"
+                    ]
+            found = [f"{labels[1][0]}={sides[1]}",
+                     f"{labels[2][0]}={sides[2]}",
+                     f"{labels[2][1]}={angles[2]*180/pi}^\\circ"
+                    ]
+        else:
+            #ASA
+            given = [f"{labels[2][1]}={angles[2]*180/pi}^\\circ",
+                     f"{labels[1][1]}={angles[1]*180/pi}^\\circ",
+                     f"{labels[0][0]}={sides[0]}"
+                    ]
+            found = [f"{labels[1][0]}={sides[1]}",
+                     f"{labels[2][0]}={sides[2]}",
+                     f"{labels[0][1]}={angles[0]*180/pi}^\\circ"
+                    ]
+
+        shuffle(given)
+        tasks.append({"given": ",".join(given[:-1])+r",\text{ and }"+given[-1], 
+                      "found": ",".join(found[:-1])+r",\text{ and }"+found[-1],
+                    })
+
+
+        #Ambiguous case
+        angles=[choice([10,15,..,70])*pi/180]
+        #If A is too big and b is too short, no integer values for a work 
+        minb=int(2/(1-sin(angles[0])))+1
+        b=choice([max(5,minb),..,max(15,minb+5)])
+        labels=[("a","A"),("b","B"),("c","C")]
+        shuffle(labels)
+        if choice([True,False]):
+            #Two solutions
+            a=choice([floor(b*sin(angles[0]))+1..b-1])
+            sides=[a,b]
+            B=arcsin(sides[1]/sides[0]*sin(angles[0]))
+            angles1=[angles[0],B,pi-angles[0]-B]
+            angles2=[angles[0],pi-B,B-angles[0]]
+            sides1=sides+[round(sqrt(sides[0]^2+sides[1]^2-2*sides[0]*sides[1]*cos(angles1[2])),1)]
+            sides2=sides+[round(sqrt(sides[0]^2+sides[1]^2-2*sides[0]*sides[1]*cos(angles2[2])),1)]
+            given = [f"{labels[0][1]}={angles[0]*180/pi}^\\circ",
+                     f"{labels[0][0]}={sides[0]}",
+                     f"{labels[1][0]}={sides[1]}"
+                    ]
+            found1= [f"{labels[2][0]}={sides1[2]}",
+                     f"{labels[1][1]}={round(angles1[1]*180/pi,1)}^\\circ",
+                     f"{labels[2][1]}={round(angles1[2]*180/pi,1)}^\\circ"
+                    ] 
+            found2= [f"{labels[2][0]}={sides2[2]}",
+                     f"{labels[1][1]}={round(angles2[1]*180/pi,1)}^\\circ",
+                     f"{labels[2][1]}={round(angles2[2]*180/pi,1)}^\\circ"
+                    ] 
+            found=r"\text{There are two possiblities: }"+",".join(found1[:-1])+r",\text{ and }"+found1[-1] + r"\text{ or }" + \
+                                                 ",".join(found2[:-1])+r",\text{ and }"+found2[-1]
+
+        else:
+            #One solution
+            a=b+choice([2..10])
+            sides=[a,b]
+            angles.append(arcsin(sides[1]/sides[0]*sin(angles[0])))
+            angles.append(pi-angles[0]-angles[1])
+            sides.append(round(sqrt(sides[0]^2+sides[1]^2-2*sides[0]*sides[1]*cos(angles[2])),1))
+            given = [f"{labels[0][1]}={angles[0]*180/pi}^\\circ",
+                     f"{labels[0][0]}={sides[0]}",
+                     f"{labels[1][0]}={sides[1]}"
+                    ]
+            found = [f"{labels[2][0]}={sides[2]}",
+                     f"{labels[1][1]}={round(angles[1]*180/pi,1)}^\\circ",
+                     f"{labels[2][1]}={round(angles[2]*180/pi,1)}^\\circ"
+                    ]
+            found=",".join(found[:-1])+r",\text{ and }"+found[-1]
+
+        shuffle(given)
+        tasks.append({"given": ",".join(given[:-1])+r",\text{ and }"+given[-1], 
+                      "found": found 
+                    })
+
+
+        shuffle(tasks)
+        return { "tasks": tasks,
+        }

source/precalculus/exercises/outcomes/TE/TE5/template.xml

@@ -0,0 +1,19 @@
+<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
+    <intro>
+      <p>Solve each of the following triangles. State whether you used the law of sines 
+        or the law of cosines and explain your choice. In the case where there may be two 
+        solutions, give sufficient work/explanation to show that you checked for that 
+        possibility and give both solutions when appropriate.
+      </p>
+    </intro>
+    {{#tasks}}
+    <knowl>
+      <content>
+        <p>In triangle <m>ABC</m>, <m>{{given}}.</m> Solve the triangle, i.e. find all remaining sides and angles.</p>
+      </content>
+      <outtro>
+        <p><m>{{found}}</m></p>
+      </outtro>
+    </knowl>
+    {{/tasks}}
+</knowl>