Math Is Fun Forum

baskar

Member

Registered: 2009-06-07

Posts: 3

trigonometric equations

dear friends,
i need a solution for this sum

the smallest positive root of the equation tanx-x=0 lies in

(a) (0,pi/2)                      (b) (pi/2,pi)
(c) (pi,3pi/2)                    (d) (3pi/2,2pi)

please help me.
thanks
bhaskar

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: trigonometric equations

x and tan x coincide at x=0, but then tan x > x for 0<x<π/2. (You can check this with gradients.)

So no solution exists in (0,π/2). Clearly no solution exists in (π/2,π) either, because tan x is negative in that domain.

tan(π) = 0 and tan(3π/2) -> ∞, so within that interval some x must exist such that tanx = x (since tan is continuous within the interval).

c) is the answer.

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Why did the vector cross the road?
It wanted to be normal.

baskar

Member

Registered: 2009-06-07

Posts: 3

Re: trigonometric equations

thank you very much

sorry for the delayed reply as i haven't logged in for a while

baskar:)

riad zaidan

Guest

Re: trigonometric equations

Hi,
When plotting the graph of  y= tan(x) and  y=x the two curves do intersect at some point in the third quardenet i.e between pi and 3pi/2

w.b.w
Mr riad zaidan
Al-quds Open University
Jenin
Palistine