T formula question (1 Viewer)

matchalolz · Jul 3, 2014

so I've been doing my maths homework for once and came across a question I didn't understand.

for question 6 i've done part (a) but don't know how to do part (b). help please?

SpiralFlex · Jul 3, 2014

$t = \tan 112.5,\; $we have shown$\; \frac{2t}{1-t^2} = 1.$

Can you do something with both? If you rearrange the second, what type of equation do you get?

aDimitri · Jul 3, 2014

Leading on from a)

$\frac{2t}{1-t^{2}} = 1 \\ \text{Now, solve for t} \\ 2t = 1-t^{2} \\ t^2 + 2t - 1 = 0 \\ t = \frac{-2 \pm \sqrt{4+4}}{2} \\ t = - 1 - \sqrt{2} \\ \text{The other root represents the other value of t for which } \frac{2t}{1-t^{2}} = 1 \\ \text{That is, } \tan{22.5} = \sqrt{2} - 1$

aDimitri · Jul 3, 2014

Dammit someone always beats me by a couple of minutes while I'm typing it up with LaTeX.

QZP · Jul 3, 2014

Why do you just spoon feed answers?

matchalolz · Jul 3, 2014

aDimitri said:
Leading on from a)

$\frac{2t}{1-t^{2}} = 1 \\ \text{Now, solve for t} \\ 2t = 1-t^{2} \\ t^2 + 2t - 1 = 0 \\ t = \frac{-2 \pm \sqrt{4+4}}{2} \\ t = - 1 - \sqrt{2} \\ \text{The other root represents the other value of t for which } \frac{2t}{1-t^{2}} = 1 \\ \text{That is, } \tan{22.5} = \sqrt{2} - 1$

thanks so much! i forgot that the quadratic formula existed

ack this is slightly worrying...

aDimitri · Jul 3, 2014

QZP said:
Why do you just spoon feed answers?

I wouldn't call it spoon feeding, it's just giving a solution - because that's exactly what I'm looking for when I post a question on here.

T formula question (1 Viewer)

matchalolz

Well-Known Member

SpiralFlex

Well-Known Member

aDimitri

i'm the cook

aDimitri

i'm the cook

QZP

Well-Known Member

matchalolz

Well-Known Member

aDimitri

i'm the cook

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