Trig Sketching ? (1 Viewer)

SammyT123 · Mar 7, 2015

How exactly would you go about sketching harder trig functions? Like 1-sec^2 (x + pi/2)

Domain,
range ,
amplitude ,
phase ,
dy/dx =0,
Sign of dy/dx

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InteGrand · Mar 7, 2015

$1-\sec^2 \theta = 1-(\tan^2 \theta +1) = -\tan^2 \theta$ .

So you just need to sketch $-\tan^2 \left (x + \frac{\pi}{2} \right )$ .

InteGrand · Mar 7, 2015

Alternatively,

$\cos \left (x + \frac{\pi}{2} \right) = -\sin x$ (check the graph of cos x to verify).

So $\sec ^2 \left (x + \frac{\pi}{2} \right) =\mbox{cosec} ^2 x$ .

So the original function is $1 - \mbox{cosec} ^2 x =- \cot^2 x$ .

InteGrand · Mar 7, 2015

If you observe a graph of cot x, you should be able to sketch the graph of -cot² x.

Trig Sketching ? (1 Viewer)

SammyT123

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InteGrand

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InteGrand

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InteGrand

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