<p><strong>Tangent Curve,</strong> $y=\tan (x)$</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1768034971829-mqv0dudkg5f.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p><strong>Tangent Curve,</strong> $y=a\tan (bx)$, $a&gt;0$</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1768035011171-qd2myp9w8jf.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 150px;"><col style="width: 150px;"><col style="width: 150px;"></colgroup><thead><tr style="height: 50px;"><th style="height: 50px; min-height: 50px; text-align: center; --cell-justify: center">Function</th><th style="height: 50px; min-height: 50px; text-align: center; --cell-justify: center">Period (degrees)</th><th style="height: 50px; min-height: 50px; text-align: center; --cell-justify: center">Period (radians)</th></tr></thead><tbody><tr style="height: 70px;"><td style="height: 70px; min-height: 70px; text-align: center; --cell-justify: center">$y = 5 \tan 3x$</td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 70px;"><td style="height: 70px; min-height: 70px; text-align: center; --cell-justify: center">$y = 3 \tan 2x$</td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 70px;"><td style="height: 70px; min-height: 70px; text-align: center; --cell-justify: center">$y = \tan \frac{3}{4}x$</td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 70px;"><td style="height: 70px; min-height: 70px; text-align: center; --cell-justify: center">$y = \tan \pi x$</td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td><td style="height: 70px; min-height: 70px; text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></div>
<p class="paragraph-header">Steps of Sketching Tangent Curve</p>
<ol class="num-list"><li data-list-item-id="item-1768035039439-hssqghsr4"><div class="list-item-paragraph">Decide the number of complete cycles required. No. of cycles $\frac{\textbf{Given Domain}}{\textbf{Period}}$.</div></li><li data-list-item-id="item-1768035039927-whdejc4ja"><div class="list-item-paragraph">Draw the grids out based of on the number of complete cycles required. Take note that&nbsp;$2$ grids per cycle.<br></div></li><li data-list-item-id="item-1768035040599-4rqtzu58n"><div class="list-item-paragraph">Draw the $y$ and $x$ axes.<br></div></li><li data-list-item-id="item-1768035041078-l6nbxfjxm"><div class="list-item-paragraph">Draw the asymptotes on grid lines $ 1,3,5,7,.. \dots $</div></li><li data-list-item-id="item-1768035151984-ciuj2s3qf"><div class="list-item-paragraph">Sketch the curve.</div></li><li data-list-item-id="item-1768035041526-iqdjpsfo6"><div class="list-item-paragraph">Mark down the period and label the graph.</div></li></ol>
<p>Sketch the graph of $y=\tan \left(\frac{3}{2} x\right)$ for&nbsp;$ 0 \leq x \leq2\pi$. State the period of the function.<br><br></p>

Decide the number of complete cycles required. No. of cycles $\frac{\textbf{Given Domain}}{\textbf{Period}}$.

Draw the grids out based of on the number of complete cycles required. Take note that $2$ grids per cycle.


Draw the asymptotes on grid lines $ 1,3,5,7,.. \dots $

Mark down the period and label the graph.

Sketch the graph of $y=\tan \left(\frac{3}{2} x\right)$ for $ 0 \leq x \leq2\pi$. State the period of the function.



Sketching of $y=a\tan \left( bx \right)$

Sketching of $y=a\tan \left( bx \right)$

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