Question

Find the exact value by using a half-angle identity.
\(tan\dfrac{7\pi}{8}\)

Answer 1

ok tan(pie\8)=1-cos(pie/4) /1-sin(pie/4) thats the half angle identity right so we know now that cos(pie/4) =root2/2 similarly to sine (pie/4) so the you solve :)

Answer 2

oh sorry im really tired i messed up sorry the identity is
tan(pie/8)=1-cos(pie/4) / 1+cos(pie/4)

Answer 3

haha we meet again JESS

Answer 4

easy......which half angle formula do u want??

Answer 5

Ummmm I don't know. I have no clue on how to even start this.

Answer 6

lol

Answer 7

so I am guessing without any conversions!!

Answer 8

OK here we go

Answer 9

where do u think 7pi/8 lies

Answer 10

Is it b/w (0,pi) or (pi,2pi)??

Answer 11

cmon girl......we're losing daylight
!!

Answer 12

I think pi, 2pi

Answer 13

@sleepyjess

Answer 14

seriously??

Answer 15

when I say think I meant find the value not guess!!!

Answer 16

wake up!!

Answer 17

You can use \[\tan\left(\frac{x}{2}\right) = \frac{1-\cos(x)}{\sin(x)}\]\[\tan\left(\dfrac{7\pi}{8}\right) = \tan\left(\dfrac{\dfrac{7\pi}{4}}{2}\right)\]

Answer 18

NO @Jhannybean LET HER WAKE UP FIRST

Answer 19

there's a far better way dude

Answer 20

easier...

Answer 21

\[\tan\left(\dfrac{\color{red}{\dfrac{7\pi}{4}}}{2}\right) =\tan\left(\frac{\color{red}x}{2}\right)\]

Answer 22

still easier

Answer 23

Therefore, \[\tan\left(\frac{\color{red}x}{2}\right) = \frac{1-\cos(\color{red}x)}{\sin(\color{red}x)}\]

Answer 24

Do you understand, @sleepyjess ?

Answer 25

Kind of

Answer 26

Follow my posts please.

Answer 27

dude do u guys dont want easier versions??

Answer 28

meh...fine!!

Answer 29

Let the person learn it however he/she likes, stop enforcing your methods, please.

Answer 30

Go ahead and show her then, and stop spamming the question :)

Answer 31

So you just do tan(whatever) over 2?

Answer 32

Pretty much, there are 3 different identities for the half angle for tan. You can use whatever one you like

Answer 33

\[\tan\left(\frac{x}{2}\right) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\]\[\tan\left(\frac{x}{2}\right) = \frac{1-\cos(x)}{\sin(x)}\]\[\tan\left(\frac{x}{2}\right) = \frac{\sin(x)}{1+\cos(x)}\]

Answer 34

So, \(\sf \tan\left(\dfrac{\color{red}{\dfrac{7\pi}{4}}}{2}\right) = \sqrt{\dfrac{1-cos\dfrac{7\pi}{4}}{1+cos\dfrac{7\pi}{4}}}\)

Answer 35

I wasn't really comfortable with the square root, so I chose to use the second form instead, lol.

Answer 36

oh lol
that was a lot to type out haha

Answer 37

:) First of all, do you understand why \(\dfrac{7\pi}{8} \longrightarrow \dfrac{7\pi}{4}\) ?

Answer 38

so, \(\sf \dfrac{1-cos\dfrac{7\pi}{4}}{sin\dfrac{7\pi}{4}}\)

Answer 39

ya I get ur method @Jhannybean ..LOL

Answer 40

Because 8/4 is 2 right?

Answer 41

this method is useful for people with calculators

Answer 42

Not exactly. \[\frac{7\pi}{8} =\dfrac{\color{red}{\dfrac{7\pi}{4}}}{2}\]

Answer 43

Correction, because 8/2 is 4

Answer 44

lets say we change it to something simpler

Answer 45

pi>7pi/8>0

Answer 46

lies in second quadrant

Answer 47

Correct.

Answer 48

so tan is negative

Answer 49

now......tan 7pi/8=tan(pi-pi/8)

Answer 50

and we knw tan (pi-x)=-tanx

Answer 51

u with me gurl??

Answer 52

Yeah

Answer 53

so then we get -tan pi/8

Answer 54

now we folloy @Jhannybean

Answer 55

so we get pi/4

Answer 56

using \[\tan 2\theta = 2 \tan \theta/1-\tan^2\theta\]

Answer 57

U know this formula rt??

Answer 58

Yes, it is in my lesson

Answer 59

so know we change it

Answer 60

in terms of tan theta

Answer 61

or follow @Jhannybean whichever u get

Answer 62

Go ahead an finish up @cambrige , writing up both explanations will only confuse the person asking.

Answer 63

@Jhannybean thinks I think he is incompetent to solve problems.Fine I quit..Solve it for her

Answer 64

and stop pmming me @Jhannybean

Answer 65

ok so,...yes we were at -tan pi/8

Answer 66

on changing it for half angle

Answer 67

then we will get formula

Answer 68

tan x/2= sin x/1-cos x

Answer 69

oi........U there???

Answer 70

Yes

Answer 71

after that U get ??

Answer 72

taking x=pi/4

Answer 73

tan (pi/4)/2=

Answer 74

sin (pi/4)/1-cos pi/4

Answer 75

mind telling me the value of cos and sin pi/4???

Answer 76

okay.......Me waiting??

Answer 77

@sleepyjess