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---+ Trig Diagnostic Test

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---++ Trig
__Answer the following questions without calculators or trig tables.%BR%\
Leave answers like <latex> 53 \pi </latex> or <latex> \sin{13^{\circ}}</latex> as is.__
---+++ !!1. Convert:
---++++ !!a. <latex> 30^{\circ}</latex> to radians.
%BEGINANSWER%
<latex>\frac{\Pi}{6}</latex>

%SHOWWORK%
   * Recall that a full circle is:%BR% <latex>= 2\Pi radians</latex>%BR%<latex>= 360^{\circ} </latex>
   * Use the principle of _Dimensional Analysis_ to convert the units:
<latex> 30^{\circ} \dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }</latex>
<latex> = \frac{60\Pi}{360} radians </latex>
<latex> = \frac{\Pi}{6} radians </latex>
%ENDANSWER%
---++++ !!b. <latex> \frac{ 3 \pi }{2} radians</latex> to degrees.
---++++ !!c. <latex> 127^{\circ} </latex> to radians.
---+++ !!2. Evaluate:
---++++ !!a. <latex>\sin{60^{\circ}}</latex>
---++++ !!b. <latex>\tan{\frac{3\pi}{4}}</latex>
---++++ !!c. <latex>\sec{\frac{pi}{2}}</latex>
---+++ !!3. Sketch the graph of <latex>\sin(x)</latex>%BR%
       (Make your vertical scale as large as possible.)
---+++ !!4. Given <latex>\mbox{ \small $\tan{\theta}  = \frac{6}{7}$ }</latex>, find <latex>\sin{\theta}</latex>
---+++ !!5. Solve the following right triangle:%BR%
       ( _i.e._ determine missing sides and angles.)
---++++ !!a. %$\overline{AB} = $%
---++++ !!b. %$\overline{AC} = $%
---++++ !!c. %$\angle{A} = $%
---+++ !!6. Relate to  <latex>\sin( \theta ) </latex>  and  <latex> \cos( \theta ) </latex>
---++++ !!a.  <latex>\cos(-\theta)</latex>
---++++ !!b.  <latex>\sin(\frac{\pi}{2} -\theta)</latex>
---++++ !!c.  <latex>\sin(2 \cdot \theta)</latex>
---+++ !!7. Express in terms of  <latex>\sin()</latex>  and  <latex>\cos()</latex> of  =A= and  =B= :

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-- Main.DickFurnas - 21 Apr 2007