Question

How do you find the solution to `csctheta-1=3csctheta-11` if `0<=theta<2pi`?

Answer 1

`theta~~ 0.20136 , 2.9402` radians

Explanation:

`csc(theta)-1=3csctheta-11`

`csctheta-3csctheta=-11=1`

`2csctheta=10=>csctheta=5`

`csctheta=1/sintheta`

`:.`

`1/sintheta=5`

`sintheta=1/5=> theta~~ 0.20136 , 2.9402` radians

Answer 2

`11^@54; 168^@46`

Explanation:

Transform equation in terms of sin t:
`1/sin t - 1 = 3/sin t - 11`
`10 = 2/sin t`
`sin t = 2/10 = 1/5`
Calculator and unit circle give:
`t = 11^@54` and `t = 180 - 11.54 = 168^@46`