TR1 feedback on first draft

source/precalculus/source/06-TR/01.ptx

@@ -17,15 +17,15 @@
         <p>
           An <term>angle</term> is formed by joining two rays at their starting points.
           The point where they are joined is called the <term> vertex</term> of the angle.
-          The measure of an angle is the amount of a circle between the two rays. 
+          The measure of an angle describes the amount of rotation between the two rays. 
         </p>
       </statement>
     </definition>
 
     <activity>
       <introduction>
         <p>
-          We know that if you complete a full turn of the circle the angle created will be 360 degrees.  Use this to estimate the measure of the given angles.
+          An angle that is rotated all the way around back to its starting point measures <m>360^\circ</m>, like a circle.  Use this to estimate the measure of the given angles.
 
         </p>
       </introduction>
@@ -38,7 +38,7 @@ TBIL.plot_angle(pi/2,reference_angle=pi/4,show_axes=False)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>45^{\circ}</m> </p></li>
             <li><p> <m>90^{\circ}</m> </p></li>
             <li><p> <m>135^{\circ}</m> </p></li>
@@ -60,7 +60,7 @@ TBIL.plot_angle(pi,reference_angle=-pi/6,show_axes=False)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>45^{\circ}</m> </p></li>
             <li><p> <m>90^{\circ}</m> </p></li>
             <li><p> <m>135^{\circ}</m> </p></li>
@@ -82,7 +82,7 @@ TBIL.plot_angle(135*pi/180,reference_angle=pi/2,show_axes=False)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>45^{\circ}</m> </p></li>
             <li><p> <m>90^{\circ}</m> </p></li>
             <li><p> <m>135^{\circ}</m> </p></li>
@@ -122,7 +122,7 @@ TBIL.plot_angle(-3*pi/4)
     <activity>
       <introduction>
         <p>
-         Find the measure of the angles drawn in standard position.
+         Estimate the measure of the angles drawn in standard position.
         </p>
       </introduction>
       <task>
@@ -134,7 +134,7 @@ TBIL.plot_angle(pi/4)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>45^{\circ}</m> </p></li>
             <li><p> <m>90^{\circ}</m> </p></li>
             <li><p> <m>135^{\circ}</m> </p></li>
@@ -156,7 +156,7 @@ TBIL.plot_angle(-pi)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>180^{\circ}</m> </p></li>
             <li><p> <m>90^{\circ}</m> </p></li>
             <li><p> <m>-180^{\circ}</m> </p></li>
@@ -179,7 +179,7 @@ TBIL.plot_angle(-5*pi/6)
           </sageplot>
         </image>
         <p>
-          <ol marker="A." cols="2">
+          <ol marker="A." cols="4">
             <li><p><m>30^{\circ}</m> </p></li>
             <li><p> <m>-150^{\circ}</m> </p></li>
             <li><p> <m>-210^{\circ}</m> </p></li>
@@ -188,7 +188,7 @@ TBIL.plot_angle(-5*pi/6)
         </statement>
         <answer>
           <p>
-            D
+            B
           </p>
         </answer>
       </task>
@@ -209,18 +209,51 @@ TBIL.plot_angle(-225*pi/180)
 
     <remark>
     <p>
+      Degrees are not the only way to measure an angle. We can also describe the angle's measure by the amount of the circumference of the circle that the angle's rotation created. We'll need to define a few terms to help us come up with this new measurement. 
+     </p>
+     <!-- <p>  
+      Recall that the circumference of a circle is given by <m>C=2\pi r</m>, where <m>r</m> is the radius of the circle. FINISH THIS!
       Activity or remark - Something about the circumference of a circle being another way to measure the angle.  <m>C=2\pi r</m> divide both sides by the radius, so a full circle or <m>360^{\circ}=2\pi</m> radians
-    </p>
+    </p> -->
     </remark>
 
+    <definition xml:id="def-central-angle">
+      <statement>
+        <p>
+          A <term>central angle</term> is an angle whose vertex is at the center of a circle.
+        </p>
+
+<image width="50%">
+  <sageplot>
+<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
+p=TBIL.plot_angle(2*pi/3,show_unit_circle=True,show_angle_value=False,degree_labels=False)
+p
+  </sageplot> 
+</image>  
+      </statement>
+    </definition>
+
+
+
     <definition xml:id="def-radian">
       <statement>
         <p>
           One <term>radian</term> is the measure of a central angle of a circle that intersects an arc the same length as the radius.
         </p>
+
+         <!-- image below needs adjusting to highlight the length of the radius on the x-axis and the arc and label them as having the same distance s -->
+<image width="50%">
+  <sageplot>
+<xi:include parse="text" href="../../../common/sagemath/library.sage"/>
+p=TBIL.plot_angle(1,show_unit_circle=True,show_angle_value=False,degree_labels=False)
+p
+  </sageplot> 
+</image>  
       </statement>
     </definition>
 
+
+
     <activity>
       <introduction>
         <p>
@@ -311,4 +344,4 @@ TBIL.plot_angle(-225*pi/180)
         <title>Videos</title>
         <p>It would be great to include videos down here, like in the Calculus book!</p>
     </subsection> -->
-</section>
+</section>