Implement Errata Rcv'd Nov-Dec (Precal Trio 2e's)

openstax · Mar 25, 2024 · 1ad4725 · 1ad4725
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diff --git a/media/CNX_Precalc_Figure_08_04_023n.jpg b/media/CNX_Precalc_Figure_08_04_023n.jpg
diff --git a/modules/m49327/index.cnxml b/modules/m49327/index.cnxml
@@ -585,7 +585,7 @@
 </m:mtr>
 <m:mtr>
 <m:mtd>
-<m:mi>r</m:mi><m:mo>=</m:mo><m:mn>−0.970</m:mn>
+<m:mi>r</m:mi><m:mo>=</m:mo><m:mn>0.970</m:mn>
 </m:mtd>
 </m:mtr>
 </m:mtable>

diff --git a/modules/m49346/index.cnxml b/modules/m49346/index.cnxml
@@ -4147,7 +4147,7 @@ of a polynomial function in the form <m:math>
   </m:msub>
   <m:mi>x</m:mi><m:mo>+</m:mo><m:msub>
    <m:mi>a</m:mi>
-   <m:mn>1</m:mn>
+   <m:mn>0</m:mn>
   </m:msub>
 </m:mrow>
 </m:math>

diff --git a/modules/m49371/index.cnxml b/modules/m49371/index.cnxml
@@ -2828,6 +2828,8 @@ Now we draw a 45° angle on the two circles, as in <link target-id="Figure_05_01
   <problem id="fs-id1165135689542">
    <para id="fs-id1165135689545">415°</para></problem>
  </exercise>
+
+ <para id="para-00002">For the following exercises, draw an angle in standard position with the given measure as well as a coterminal angle.</para>
 <exercise id="fs-id1165134547254"><problem id="fs-id1165134547256">
   <para id="fs-id1165134547258">−120°</para>
  </problem>

diff --git a/modules/m49393/index.cnxml b/modules/m49393/index.cnxml
@@ -1,9 +1,9 @@
 <document xmlns="http://cnx.rice.edu/cnxml" xmlns:m="http://www.w3.org/1998/Math/MathML">
 
-<title>Solving Trigonometric Equations with Identities</title>
+<title>Simplifying and Verifying Trigonometric Identities</title>
 <metadata xmlns:md="http://cnx.rice.edu/mdml">
   <md:content-id>m49393</md:content-id>
-  <md:title>Solving Trigonometric Equations with Identities</md:title>
+  <md:title>Simplifying and Verifying Trigonometric Identities</md:title>
   <md:abstract><para id="para-00001">In this section, you will:</para><list id="list-00001">
 <item>Verify the fundamental trigonometric identities.</item>
 <item>Simplify trigonometric expressions using algebra and the identities.</item>
@@ -1417,7 +1417,7 @@ For example, consider corresponding inputs <m:math>
 </equation>
 </note><example id="Example_07_01_01">
 <exercise id="fs-id1194554"><problem id="fs-id1616347">
-<title>Graphing the Equations of an Identity</title>
+<title>Graphing the Expressions of an Identity</title>
 <para id="fs-id1693457">Graph both sides of the identity <m:math>
 <m:mrow>
 <m:mi>cot</m:mi><m:mspace width="0.3em"/><m:mi>θ</m:mi><m:mo>=</m:mo><m:mfrac>

diff --git a/modules/m49395/index.cnxml b/modules/m49395/index.cnxml
@@ -4086,7 +4086,7 @@
 
   </section><section id="fs-id1926444">
     <title>Using the Sum and Difference Formulas to Verify Identities</title>
-    <para id="fs-id2637951">Verifying an identity means demonstrating that the equation holds for all values of the variable. It helps to be very familiar with the identities or to have a list of them accessible while working the problems. Reviewing the general rules from <link document="m49393">Solving Trigonometric Equations with Identities</link> may help simplify the process of verifying an identity.</para><note id="fs-id2637962" class="how-to-notitle">
+    <para id="fs-id2637951">Verifying an identity means demonstrating that the equation holds for all values of the variable. It helps to be very familiar with the identities or to have a list of them accessible while working the problems. Reviewing the general rules from <link document="m49393">Simplifying and Verifying Trigonometric Identities</link> may help simplify the process of verifying an identity.</para><note id="fs-id2637962" class="how-to-notitle">
       <label>How To</label>
       <para id="fs-id1863876"><emphasis>Given an identity, verify using sum and difference formulas.</emphasis></para><list id="fs-id1863880" list-type="enumerated" number-style="arabic">
         <item>Begin with the expression on the side of the equal sign that appears most complex. Rewrite that expression until it matches the other side of the equal sign. Occasionally, we might have to alter both sides, but working on only one side is the most efficient.</item>

diff --git a/modules/m49399/index.cnxml b/modules/m49399/index.cnxml
@@ -5369,7 +5369,7 @@ Spring 2 comes to rest first after 7.3 seconds.
 </para>
 </solution></exercise></section>
 </section>
-<section id="fs-id1817053" class="review-exercises"><title>Chapter Review Exercises</title><section id="fs-id1817056"><title><link document="m49393">Solving Trigonometric Equations with Identities</link></title><para id="fs-id1817061">For the following exercises, find all solutions exactly that exist on the interval <m:math>
+<section id="fs-id1817053" class="review-exercises"><title>Chapter Review Exercises</title><section id="fs-id1817056"><title><link document="m49393">Simplifying and Verifying Trigonometric Identities</link></title><para id="fs-id1817061">For the following exercises, find all solutions exactly that exist on the interval <m:math>
     <m:mrow>
      <m:mrow><m:mo>[</m:mo> <m:mrow>
       <m:mn>0</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mi>π</m:mi>

diff --git a/modules/m49407/index.cnxml b/modules/m49407/index.cnxml
@@ -3590,7 +3590,7 @@ increases at a constant rate in an ever-widening, never-ending, spiraling path.
 </section>
   <section id="fs-id1165134301472">
     <title>Summary of Curves</title>
-    <para id="fs-id1165133192927">We have explored a number of seemingly complex polar curves in this section. <link target-id="Figure_08_04_023"/> and <link target-id="Figure_08_04_024"/> summarize the graphs and equations for each of these curves.</para><figure id="Figure_08_04_023"><media id="fs-id1165135641462" alt="Four graphs side by side - a summary. (A) is a circle: r=asin(theta) or r=acos(theta). (B) is a cardioid: r= a + or - bcos(theta), or r = a + or - b sin(theta). a>0, b>0, a/b=1. (C) is inner-loop limaçons. r= a + or - bcos(theta), or r= a + or - bsin(theta). a>0, b>0, 1&lt;a/b&lt;2. (D) is inner-loop limaçons. R = a + or - bcos(theta), or r = a + or - bsin(theta). A>0, b>0, a&lt;b.">
+    <para id="fs-id1165133192927">We have explored a number of seemingly complex polar curves in this section. <link target-id="Figure_08_04_023"/> and <link target-id="Figure_08_04_024"/> summarize the graphs and equations for each of these curves.</para><figure id="Figure_08_04_023"><media id="fs-id1165135641462" alt="Four graphs side by side - a summary. (A) is a circle: r=asin(theta) or r=acos(theta). (B) is a cardioid: r= a + or - bcos(theta), or r = a + or - b sin(theta). a>0, b>0, a/b=1. (C) is one-loop limaçons. r= a + or - bcos(theta), or r= a + or - bsin(theta). a>0, b>0, 1&lt;a/b&lt;2. (D) is inner-loop limaçons. R = a + or - bcos(theta), or r = a + or - bsin(theta). A>0, b>0, a&lt;b.">
         <image mime-type="image/jpg" src="../../media/CNX_Precalc_Figure_08_04_023n.jpg"/>
       </media>
     </figure><figure id="Figure_08_04_024"><media id="fs-id1165137419023" alt="Four graphs side by side - a summary. (A) is lemniscates. R^2 = a^2cos(2theta), or r^2=a^2sin(2theta). a is not equal to 0. (B) is a rsose curve (n even). R = acos(ntheta), or r=asin(ntheta). N is even, and there are 2n petals. (C) is a rose curve (n odd). R = acos(ntheta), or r=asin(theta). N is odd, and there are n petals. (D) is an Archimedes's spiral. R=theta, and theta >=0.">

diff --git a/modules/m50389/index.cnxml b/modules/m50389/index.cnxml
@@ -2117,7 +2117,7 @@
 
 <exercise id="fs-id1165135168173">
 <problem id="fs-id1165135168176">
-<para id="fs-id1165135168178"> <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mo>−</m:mo><m:mn>4</m:mn><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>1</m:mn></m:mrow></m:math> </para>
+<para id="fs-id1165135168178"> <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mo>−</m:mo><m:mn>3</m:mn><m:mi>x</m:mi><m:mo>−</m:mo><m:mn>1</m:mn></m:mrow></m:math> </para>
 </problem>
 <solution id="fs-id1165134340072">
 <para id="fs-id1165135615907">F</para>

diff --git a/modules/m51272/index.cnxml b/modules/m51272/index.cnxml
@@ -855,7 +855,7 @@
      <m:mtr columnalign="left">
       <m:mtd columnalign="left">
        <m:mrow>
-        <m:mspace width="0.5em"/><m:mtext/><m:mi>r</m:mi><m:mo>=</m:mo><m:mn>−0.970</m:mn>
+        <m:mspace width="0.5em"/><m:mtext/><m:mi>r</m:mi><m:mo>=</m:mo><m:mn>0.970</m:mn>
        </m:mrow>
       </m:mtd>
      </m:mtr>

diff --git a/modules/m51274/index.cnxml b/modules/m51274/index.cnxml
@@ -3828,7 +3828,7 @@ symmetry: x = 3, intercepts:
 </para>
 
   <media id="fs-id1165134391611" alt="Graph of f(x)=4x^2-12x-3">
-    <image mime-type="image/jpg" src="../../media/CNX_Precalc_Figure_03_02_206.jpg"/>
+    <image mime-type="image/jpg" src="../../media/CNX_Precalc_Figure_05_01_237.jpg"/>
     </media>
 
 </solution></exercise>
@@ -3921,7 +3921,7 @@ symmetry: x = 3, intercepts:
    </m:mfrac>
    <m:mo>, </m:mo> <m:mn>0</m:mn><m:mo>)</m:mo>
    </m:math>
-   <media id="eip-idm381174624" alt=""><image mime-type="jpeg" src="../../media/CNX_Precalc_Figure_05_01_237.jpg"/></media></para>
+   <media id="eip-idm381174624" alt=""><image mime-type="jpeg" src="../../media/CNX_Precalc_Figure_03_02_206.jpg"/></media></para>
 
 
 

diff --git a/modules/m51283/index.cnxml b/modules/m51283/index.cnxml
@@ -3441,6 +3441,8 @@
  </m:math>
   </para></problem>
  </exercise>
+
+ <para id="para-00002">For the following exercises, draw an angle in standard position with the given measure as well as a coterminal angle.</para>
 <exercise id="fs-id2571932"><problem id="fs-id2571934"><para id="fs-id2571936"> <m:math>
   <m:mrow>
   <m:mn>−120°</m:mn>

diff --git a/modules/m51288/index.cnxml b/modules/m51288/index.cnxml
@@ -1454,7 +1454,7 @@ For example, consider corresponding inputs <m:math>
 </equation>
 </note><example id="Example_07_01_01">
 <exercise id="fs-id1194554"><problem id="fs-id1616347">
-<title>Graphing the Equations of an Identity</title>
+<title>Graphing the Expressions of an Identity</title>
 <para id="fs-id1693457">Graph both sides of the identity <m:math>
 <m:mrow>
 <m:mi>cot</m:mi><m:mspace width="0.3em"/><m:mi>θ</m:mi><m:mo>=</m:mo><m:mfrac>

diff --git a/modules/m51292/index.cnxml b/modules/m51292/index.cnxml
@@ -6792,7 +6792,7 @@
 <exercise id="fs-id1468175"><problem id="fs-id1468176"><para id="fs-id1468177">A 23-foot ladder is positioned next to a house. If the ladder slips at 7 feet from the house when there is not enough traction, what angle should the ladder make with the ground to avoid slipping?</para></problem></exercise>
 </section>
 </section>
-<section id="fs-id1817053" class="review-exercises"><title>Chapter Review Exercises</title><section id="fs-id1817056"><title><link document="m51288">Solving Trigonometric Equations with Identities</link></title><para id="fs-id1817061">For the following exercises, find all solutions exactly that exist on the interval <m:math>
+<section id="fs-id1817053" class="review-exercises"><title>Chapter Review Exercises</title><section id="fs-id1817056"><title><link document="m51288">Simplifying and Verifying Trigonometric Identities</link></title><para id="fs-id1817061">For the following exercises, find all solutions exactly that exist on the interval <m:math>
     <m:mrow>
      <m:mspace width="0.3em"/><m:mrow><m:mo>[</m:mo> <m:mrow>
       <m:mn>0</m:mn><m:mo>,</m:mo><m:mn>2</m:mn><m:mi>π</m:mi>