Math Is Fun Forum

CidroN

Member

Registered: 2005-09-24

Posts: 1

solve tan, sin & cos

I) tan v = -1

II) 2 - tan v = 0

III) 2 tan v + 5 = 0

IV) sin x = tan x

V) 2 sin x = tan x

Thanks for help!

abhishek_rttc

Member

Registered: 2005-07-25

Posts: 6

Re: solve tan, sin & cos

I) tan v= -1 = tan (- π/4)
   Particualr Value, v= -π/4
   General Value,   v= nπ - π/4, where n=0,1,2,.....

II) tan v= 2 = tan (63.4349...)
   Particualr Value, v= tan^-1(2)
   General Value,   v= nπ +tan^-1(2), where n=0,1,2,.....

III) tan v= 5/2 = tan (68.1986...)
   Particualr Value, v= tan^-1(5/2)
   General Value,   v= nπ +tan^-1(5/2), where n=0,1,2,....

IV) sin x = tan x
     sin x cos x - sinx = 0  ( as tan x = sin x/ cos x )
     sin x (cos x -1) =0
     either sin x = 0 to cos x = 1
     in general  x = nπ, where n= 0,1,2,....

V)  2sin x = tan x
     2 sin x cos x - sinx = 0  ( as tan x = sin x/ cos x )
     sin x (2 cos x -1) =0
     either sin x = 0 to cos x = 1/2
     if sin x = 0, in general  x = nπ, where n= 0,1,2,...
     if cos x = 1/2, in general x = 2nπ +/- π/3, n= 0,1,2,...

  Hence either x = nπ or x = 2nπ +/- π/3, n= 0,1,2,...

Last edited by abhishek_rttc (2005-10-03 21:13:03)