Homework Help

How to solve the equation square root 3*sin x-cosx=0?

user profile pic

doorsreb | Student, Grade 11 | (Level 2) eNoter

Posted June 8, 2011 at 11:41 PM via web

dislike 1 like

How to solve the equation square root 3*sin x-cosx=0?

2 Answers | Add Yours

user profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted June 8, 2011 at 11:44 PM (Answer #1)

dislike 1 like

First, we'll shift cos x to the right side:

sqrt3*sin x = cos x

We'll divide by cos x both sides:

sqrt3*sin x/cos x = 1

But the fraction sin x/cos x can be replaced by the tangent function tan x.

sqrt3*tan x = 1

tan x = 1/sqrt3

Since it is not allowed to keep the square root to denominator, we'll multiply both, numerator and denominator, by sqrt3.

tan x = sqrt3/3

x = arctan (sqrt3/3) + k*pi

x = pi/6 + k*pi

The set of solutions of the equation is: {pi/6 + k*pi}.

user profile pic

chrisbond437 | Student, Grade 10 | (Level 1) Honors

Posted June 16, 2011 at 8:43 PM (Answer #2)

dislike 1 like

sin x/cos x=1/sqrt(3)

tan x=1/sqrt 3

we know tan 30=1/sqrt 3


Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes