Homework Help

Find all (theta) 0<(theta)<2pi, Such that: CSC(theta)= -2

user profile pic

rapsplash | Student, Undergraduate | (Level 1) eNoter

Posted May 13, 2012 at 8:48 PM via web

dislike 2 like

Find all (theta) 0<(theta)<2pi, Such that:


CSC(theta)= -2

1 Answer | Add Yours

user profile pic

thilina-g | College Teacher | (Level 1) Educator

Posted May 13, 2012 at 9:21 PM (Answer #1)

dislike 1 like

`cosec(theta) = -2`

we know, `cosec(theta) = 1/sin(theta)` , then,

`1/sin(theta) =-2`

This gives,

`sin(theta) = -1/2`

`theta = sin^(-1)(-1/2)`

`theta = -pi/6`

This is the primary solution, to find the solutions in the given range, we need to know the general solution for sine.

The general solution for sine is,

`theta = npi+(-1)^n(-pi/6)`   n is any integer.

n = 0,

`theta = -pi/6`

n =1,

`theta = pi + pi/6 = (7pi)/6`

n = 2,

`theta = 2pi - pi/6 = (11pi)/6`

 

Therefore the solutions in the given range, `0lt=theta lt=2pi ` are,

`(7pi)/6 and (11pi)/6`

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes