Question

use the half angle formula for tan 7 pi/8

Answer 1

\[\huge \tan\left(\frac{7\pi}{8}\right) \quad = \quad \tan\left(\frac{\left(\frac{7\pi}{4}\right)}{2}\right)\]Understand what I did there? :)
We can apply the Half Angle Formula while it's in this form.

Answer 2

yes i understand

Answer 3

Ummm do you remember the half angle formula for tangent? I think there are 2 of them :) One sec lemme look em up real quick.

Answer 4

\[\huge \tan\left(\frac{\theta}{2}\right)=\frac{1-\cos \theta}{\sin \theta}\]Mm k let's use this one :D

Answer 5

okay

Answer 6

From here the setup shouldn't be too bad. Just make sure you understand What part of your angle is THETA.

And from there we just need to remember a few special angles.

Answer 7

\[\large \tan\left(\frac{\left(\frac{7\pi}{4}\right)}{2}\right)\quad =\quad \frac{1-\cos\left(\frac{7\pi}{4}\right)}{\sin\left(\frac{7\pi}{4}\right)}\]Understand how to plug those in alright? :D

Answer 8

Just gotta remember your unit circle from here! Then a tiny bit of simplification.

Answer 9

oh yes, thank you. I can do it from here. Just a question though. In the first step I was taught to multiply by 2 because the given is half of what I need to use (i did that for degrees). Why did you divide by two instead?

Answer 10

\[\huge \left(\frac{7\pi}{8}\right) \quad \rightarrow \quad \left(\frac{\frac{2\cdot 7\pi}{8}}{2}\right)\]If you're multiplying it by 2, and then rewriting it as a half angle, you're essentially multiplying by 2, and dividing by 2 at the same time. But we save the divide for later, so we can view it as a half angle.

This is important because it doesn't change the VALUE of the angle, just the way it looks.
The way I was doing it? ummmm

Answer 11

\[\huge \left(\frac{7\pi}{8}\right) \quad \rightarrow \quad \left(\frac{7\pi}{4\cdot 2}\right)\]And then I do a little thinking, in order to write it as a fraction above a fraction. :O

Answer 12

Maybe that was is a little confusing though, I'm not sure... You have to be kind of comfortable with your fraction math :D

Answer 13

i think i did something wrong. the answer is supposed to be what it says on the bottom right