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	<title>Comments on: Trigonometry Type R</title>
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	<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r</link>
	<description>Sassy O Level Maths Tuition, Questions &#38; Tips from Singapore&#039;s Favourite Private Tutor</description>
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		<title>By: Hermes Chong</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-40340</link>
		<dc:creator>Hermes Chong</dc:creator>
		<pubDate>Mon, 30 Jan 2012 08:51:52 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-40340</guid>
		<description>&lt;span class=&quot;topsy_trackback_comment&quot;&gt;&lt;span class=&quot;topsy_twitter_username&quot;&gt;&lt;span class=&quot;topsy_trackback_content&quot;&gt;@Im__Rachelx3 http://t.co/I9bQLPwL not so accurate but what is needed is there unless is not this R formula you talking about.&lt;/span&gt;&lt;/span&gt;</description>
		<content:encoded><![CDATA[<p><span class="topsy_trackback_comment"><span class="topsy_twitter_username"><span class="topsy_trackback_content">@Im__Rachelx3 <a href="http://t.co/I9bQLPwL" rel="nofollow">http://t.co/I9bQLPwL</a> not so accurate but what is needed is there unless is not this R formula you talking about.</span></span></span></p>
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		<title>By: Kwek Seowmeng</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39445</link>
		<dc:creator>Kwek Seowmeng</dc:creator>
		<pubDate>Sun, 30 Oct 2011 06:59:58 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39445</guid>
		<description>&lt;span class=&quot;topsy_trackback_comment&quot;&gt;&lt;span class=&quot;topsy_twitter_username&quot;&gt;&lt;span class=&quot;topsy_trackback_content&quot;&gt;@ValerieLim_ @Limshinru http://t.co/yrijAs4S&lt;/span&gt;&lt;/span&gt;</description>
		<content:encoded><![CDATA[<p><span class="topsy_trackback_comment"><span class="topsy_twitter_username"><span class="topsy_trackback_content">@ValerieLim_ @Limshinru <a href="http://t.co/yrijAs4S" rel="nofollow">http://t.co/yrijAs4S</a></span></span></span></p>
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		<title>By: MA</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39331</link>
		<dc:creator>MA</dc:creator>
		<pubDate>Mon, 10 Oct 2011 07:36:25 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39331</guid>
		<description>&lt;span class=&quot;topsy_trackback_comment&quot;&gt;&lt;span class=&quot;topsy_twitter_username&quot;&gt;&lt;span class=&quot;topsy_trackback_content&quot;&gt;@colour_pencils http://t.co/dMwILudw hahah idk how to explain cuz i dun have my phone xD&lt;/span&gt;&lt;/span&gt;</description>
		<content:encoded><![CDATA[<p><span class="topsy_trackback_comment"><span class="topsy_twitter_username"><span class="topsy_trackback_content">@colour_pencils <a href="http://t.co/dMwILudw" rel="nofollow">http://t.co/dMwILudw</a> hahah idk how to explain cuz i dun have my phone xD</span></span></span></p>
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		<title>By: Miss Loi</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39314</link>
		<dc:creator>Miss Loi</dc:creator>
		<pubDate>Wed, 28 Sep 2011 05:56:58 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39314</guid>
		<description>Hello and welcome to J&#966;ss Sticks, Ray!

From parts 2(i) &amp; 2(iii) of the workings &lt;a href=&quot;#comment-15062&quot; rel=&quot;nofollow&quot;&gt;here&lt;/a&gt;, 
&lt;var&gt;OM&lt;/var&gt; = √40 cos (&lt;var&gt;θ&lt;/var&gt;+18.43&#176;)
&lt;var&gt;AM&lt;/var&gt; = √40 sin (&lt;var&gt;θ&lt;/var&gt;+18.43&#176;)

This means that both the lengths of &lt;var&gt;OM&lt;/var&gt; and &lt;var&gt;AM&lt;/var&gt; are dependent on the same angle &lt;var&gt;θ&lt;/var&gt;, which, looking at the equations above, means that both cannot be maximum at the same value of &lt;var&gt;θ&lt;/var&gt; 

i.e. When &lt;var&gt;OM&lt;/var&gt; is maximized when cos (&lt;var&gt;θ&lt;/var&gt; + &lt;var&gt;α&lt;/var&gt;) = 1, &lt;var&gt;AM&lt;/var&gt; is actually &lt;em&gt;minimized&lt;/em&gt; at this same value of &lt;var&gt;θ&lt;/var&gt; since sin (&lt;var&gt;θ&lt;/var&gt; + &lt;var&gt;α&lt;/var&gt;) = 0.

So the key here is we need an intermediate value of &lt;var&gt;θ&lt;/var&gt; that will maximize the area instead of the individual lengths hence we have to obtain the &lt;em&gt;ONE&lt;/em&gt; &lt;var&gt;R&lt;/var&gt;-formula for the area using the double-angle formula etc.</description>
		<content:encoded><![CDATA[<p>Hello and welcome to J&phi;ss Sticks, Ray!</p>
<p>From parts 2(i) &#038; 2(iii) of the workings <a href="#comment-15062" rel="nofollow">here</a>,<br />
<var>OM</var> = √40 cos (<var>θ</var>+18.43&deg;)<br />
<var>AM</var> = √40 sin (<var>θ</var>+18.43&deg;)</p>
<p>This means that both the lengths of <var>OM</var> and <var>AM</var> are dependent on the same angle <var>θ</var>, which, looking at the equations above, means that both cannot be maximum at the same value of <var>θ</var> </p>
<p>i.e. When <var>OM</var> is maximized when cos (<var>θ</var> + <var>α</var>) = 1, <var>AM</var> is actually <em>minimized</em> at this same value of <var>θ</var> since sin (<var>θ</var> + <var>α</var>) = 0.</p>
<p>So the key here is we need an intermediate value of <var>θ</var> that will maximize the area instead of the individual lengths hence we have to obtain the <em>ONE</em> <var>R</var>-formula for the area using the double-angle formula etc.</p>
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		<title>By: Ray</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39311</link>
		<dc:creator>Ray</dc:creator>
		<pubDate>Tue, 27 Sep 2011 06:38:01 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-39311</guid>
		<description>Hi Miss Loi,

I love your site and your sense of humour, definitely very localised.

Anyway, a quick question to your type-R question 2, the part on maximum area of the triangle.

Should we apply the maximum value of R at the length stage? meaning to AM and OM individually instead of applying to the area straghit?

The maximum value of AM and OM exist when cos (&#952; + &#945;) =1, Hence, maximum value for AM and OM should be &#8730;40. Hence, 1/2 times AM times OM should give us 20cm sq.?

I&#039;m confused. Pls clarify if you can? Thanks! =]</description>
		<content:encoded><![CDATA[<p>Hi Miss Loi,</p>
<p>I love your site and your sense of humour, definitely very localised.</p>
<p>Anyway, a quick question to your type-R question 2, the part on maximum area of the triangle.</p>
<p>Should we apply the maximum value of R at the length stage? meaning to AM and OM individually instead of applying to the area straghit?</p>
<p>The maximum value of AM and OM exist when cos (&theta; + &alpha;) =1, Hence, maximum value for AM and OM should be &radic;40. Hence, 1/2 times AM times OM should give us 20cm sq.?</p>
<p>I'm confused. Pls clarify if you can? Thanks! =]</p>
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		<title>By: weijie</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38527</link>
		<dc:creator>weijie</dc:creator>
		<pubDate>Wed, 10 Nov 2010 08:37:25 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38527</guid>
		<description>why cannot r be negative 5 in the exaple given ?</description>
		<content:encoded><![CDATA[<p>why cannot r be negative 5 in the exaple given ?</p>
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		<title>By: Miss Loi</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38491</link>
		<dc:creator>Miss Loi</dc:creator>
		<pubDate>Mon, 01 Nov 2010 15:24:23 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38491</guid>
		<description>If Miss Loi gets your question right ... the Factor Formulae refer to

[pmath]sin P + sin Q = 2 sin {{P+Q}/2} cos {{P-Q}/2}[/pmath]
[pmath]sin P - sin Q = 2 cos {{P+Q}/2} sin {{P-Q}/2}[/pmath]
[pmath]cos P + cos Q = 2 cos {{P+Q}/2} cos {{P-Q}/2}[/pmath]
[pmath]cos P - cos Q = -2 sin {{P+Q}/2} sin {{P-Q}/2}[/pmath]

Are they called the same thing over at Reggae Jamaica? ;)</description>
		<content:encoded><![CDATA[<p>If Miss Loi gets your question right ... the Factor Formulae refer to</p>
<p><img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_986_09e9c36d5df854ca2fac8f33026d88f8.png" style="vertical-align:-14px; display: inline-block ;" alt="sin P + sin Q = 2 sin {{P+Q}/2} cos {{P-Q}/2}" title="sin P + sin Q = 2 sin {{P+Q}/2} cos {{P-Q}/2}"/><br />
<img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_986_8149162228cba73fe8feb680be72556b.png" style="vertical-align:-14px; display: inline-block ;" alt="sin P - sin Q = 2 cos {{P+Q}/2} sin {{P-Q}/2}" title="sin P - sin Q = 2 cos {{P+Q}/2} sin {{P-Q}/2}"/><br />
<img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_986_e25277ef6655c6356d4d3ca2395c849b.png" style="vertical-align:-14px; display: inline-block ;" alt="cos P + cos Q = 2 cos {{P+Q}/2} cos {{P-Q}/2}" title="cos P + cos Q = 2 cos {{P+Q}/2} cos {{P-Q}/2}"/><br />
<img src="http://www.exampaper.com.sg/wp-content/plugins/wpmathpub/phpmathpublisher/img/math_986_cf219e6f8598d515d203b9d612db545d.png" style="vertical-align:-14px; display: inline-block ;" alt="cos P - cos Q = -2 sin {{P+Q}/2} sin {{P-Q}/2}" title="cos P - cos Q = -2 sin {{P+Q}/2} sin {{P-Q}/2}"/></p>
<p>Are they called the same thing over at Reggae Jamaica? <img src='http://www.exampaper.com.sg/blog/wp-includes/images/smilies/icon_wink.gif' alt=';)' class='wp-smiley' /> </p>
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		<title>By: Miss Loi</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38490</link>
		<dc:creator>Miss Loi</dc:creator>
		<pubDate>Mon, 01 Nov 2010 15:15:14 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38490</guid>
		<description>Are you referring to this diagram?

&lt;img src=&quot;http://www.exampaper.com.sg/blog/wp-content/uploads/2008/10/trigonometry-r-formula-question-diagram-3.gif&quot; alt=&quot;Trigonometry R-Formula Question Diagram 3&quot; /&gt;

If so, you&#039;ll find in &#916;&lt;var&gt;O&lt;/var&gt;&lt;var&gt;A&lt;/var&gt;&lt;var&gt;B&lt;/var&gt; from the diagram above that &lt;var&gt;&#952;&lt;/var&gt; &lt; 90&#176; &#8722; &lt;var&gt;&#945;&lt;/var&gt;</description>
		<content:encoded><![CDATA[<p>Are you referring to this diagram?</p>
<p><img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2008/10/trigonometry-r-formula-question-diagram-3.gif" alt="Trigonometry R-Formula Question Diagram 3" /></p>
<p>If so, you'll find in &Delta;<var>O</var><var>A</var><var>B</var> from the diagram above that <var>&theta;</var> &lt; 90&deg; &minus; <var>&alpha;</var></p>
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		<title>By: Jukie Primestein</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38429</link>
		<dc:creator>Jukie Primestein</dc:creator>
		<pubDate>Fri, 29 Oct 2010 22:33:17 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38429</guid>
		<description>which trig identity do you refer to as the factor formula?</description>
		<content:encoded><![CDATA[<p>which trig identity do you refer to as the factor formula?</p>
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		<title>By: Jukie Primestein</title>
		<link>http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38428</link>
		<dc:creator>Jukie Primestein</dc:creator>
		<pubDate>Fri, 29 Oct 2010 20:51:59 +0000</pubDate>
		<guid isPermaLink="false">http://www.exampaper.com.sg/tuition-notes/a-maths-tips/trigonometry-type-r#comment-38428</guid>
		<description>Can you please send me a few more variation of the roar R-formula.  Based on a few times I encountered it it is not always clear if you are to find a maximum or minimum!  Oh another question I have not seen any proof to convince me than cosine of a negative number is positive, but please don&#039;t get me wrong I know it is correct however a proof maybe through a diagram would really do the trick!</description>
		<content:encoded><![CDATA[<p>Can you please send me a few more variation of the roar R-formula.  Based on a few times I encountered it it is not always clear if you are to find a maximum or minimum!  Oh another question I have not seen any proof to convince me than cosine of a negative number is positive, but please don't get me wrong I know it is correct however a proof maybe through a diagram would really do the trick!</p>
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