Find the exact value of tan 22.5 by using tan 2x - Can't do. (1 Viewer)

[S1M0]

Find the exact value of tan 22.5 by using the expression tan 2x.

I don't understand how using tan 2x would solve the problem, wouldn't that just mean we have more tan 22.5s lying around?


Anyway, some clarification would be nice.

 

[undalay]

Tan 2a ?

or Tan a/2?

Coz if its half angle results simply tan(45/2) = sin 45 / 1 + cos 45

??

 

[Trebla]

Assuming you mean in degrees:

tan (2 x 22.5)= [2tan (22.5)]/[1 - tan²22.5]
tan 45 [1 - tan²22.5] = 2tan 22.5
1 - tan²22.5 = 2tan 22.5

Let x = tan 22.5
1 - x² = 2x
x² + 2x - 1 = 0
x = [- 2 ± √(8)]/2
x = - 1 ± √(2)
but: x = tan 22.5 > 0, so we take the positive root
.: tan 22.5 = - 1 + √(2)

 

[webby234]

Find the exact value of tan 22.5 by using the expression tan 2x.

I don't understand how using tan 2x would solve the problem, wouldn't that just mean we have more tan 22.5s lying around?


Anyway, some clarification would be nice.

x = 45
tan 45 = 2tan22.5/(1 - tan²22.5) = 1
1 - tan²22.5 = 2tan 22.5
tan²22.5 + 2tan 22.5 - 1 = 0
tan22.5 = -2 +/- rt(4 + 4)/2 (quadratic formula)
= -1 +/- rt2
= -1 + rt2 as it is in the first quadrant and therefore positive

 

[okhan90]

Sorry I Have To Ask... Is That Advance Maths Or Extension Cos U Juz Freaked Da Shit Outa Me Lol

 

[watatank]

maths ext 1.

 

[okhan90]

ma bad lol.. i didnt read da link LOL


farkkk man god help u guyzz.. but it seems like u kno wat u goin on about lol.. so yah

 

[S1M0]

From what i can see, i was on the right track.

Thanks for the help guys.

 

[Evergreen]

x=22.5

tan(45)= 2tan22.5/(1-tan² 22.5)= 1

2tan22.5= 1-tan² 22.5

tan² 22.5+2tan22.5-1=0

Using quadratic formula:

tan22.5= -1+ sqrt2 or -1-sqrt2

but tan22.5 is positive
.: tan22.5= -1+ sqrt2

Captain gay: formula used is the tan2A expansion which you would have/or would learn in the 3unit course.

 

[mazza!]

hey simo!