Question

\[Use~ the~inequalities~~\sin \theta<\theta<\tan \theta~~for~a~suitable~value~of~\theta\]\[\to~show~that~\pi~lies~btween~~3~~and~~2\sqrt{3}\]

Answer 1

pi/6 would work,

Answer 2

How?

Answer 3

Use \text{<text>} for text in the latex equation.

Answer 4

pi/6 = .52
sin pi/6 = .5
tan pi/6 = .577

Answer 5

Yes, but why did you think of that in the first place?

Answer 6

haha just guessed

Answer 7

That helps :p So, I need to guess? No other way?

Answer 8

i dunno, let me try to "solve it"

Answer 9

Haha. Ok :)

Answer 10

ok it turns out the inequality holds for all theta between 0 and pi/2
--> x=(0,pi/2)

http://www.wolframalpha.com/input/?i=y+%3D+sin%28x%29+-x
sin x < x, when x>0

http://www.wolframalpha.com/input/?i=y+%3D+tan%28x%29+-x
x < tan x, when 0<x<pi/2

Answer 11

Oh. OK. thanks :)