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---+ Trig Diagnostic Test %STARTINCLUDE% ---++ 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= : %STOPINCLUDE% --- -- Main.DickFurnas - 21 Apr 2007
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Topic revision: r3 - 2007-12-10
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DickFurnas
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