Trig Question (1 Viewer)

Saturn WY15 · Aug 26, 2011

Hey Guys i need help with this question

b
i) Express the tan 2θ in term's of tan θ
ii) Hence evaluate tan 22.5 degree's om surd form by letting θ= 22.5 degree's from i

Obviously i can the first question, but i don't know how to do second one.

Thanks
W.Y

SpiralFlex · Aug 26, 2011

$\tan 2(22.5^\circ ) = \frac{2\tan 22.5 ^\circ }{1-\tan^2 22.5^\circ }$

$1 = \frac{2\tan 22.5 ^\circ }{1-\tan^2 22.5^\circ }$

Let $t=\tan 22.5^\circ$

$1=\frac{2t}{1-t^2}$

$t^2+2t-1=0$

$t=\frac{-2 \pm 2\sqrt{2}}{2}$

$t=-1 \pm \sqrt{2}$

Therefore,

$t=\tan 22.5^\circ =-1 + \sqrt{2}$ ONLY! (Since it must be acute.) Very cute.

Saturn WY15 · Aug 26, 2011

Thank's alex

I knew i was on the right track, i just forget the LHS = 1

Saturn WY15 · Aug 26, 2011

accidentally put 22.5 degree as 25. Such a noob

SpiralFlex · Aug 26, 2011

No worries! Good luck with your yearly examinations.

Saturn WY15 · Aug 26, 2011

You too man, how u been ? i swear its like ages since we last talk.

SpiralFlex · Aug 26, 2011

Hungry and tired.

Trig Question (1 Viewer)

Saturn WY15

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SpiralFlex

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Saturn WY15

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Saturn WY15

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SpiralFlex

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Saturn WY15

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SpiralFlex

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