How do you find the values of $theta$ given $csctheta=(2sqrt3)/3$ ?

Question

8068 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-21T15:00:46

$theta=npi+-(-1)^npi/3$ , where $n$ is an integer.

As $csctheta=(2sqrt3)/3=2/sqrt3$

Therefore, $sintheta=sqrt3/2=sin(pi/3)$

Hence, within the interval $0 <= theta <= 2pi$ , $theta=pi/3$ or $(2pi)/3$

but as trigonometric ratios repeat after $2pi$

they are more solutions which can be put as

$theta=npi+-(-1)^npi/3$ , where $n$ is an integer.

How do you find the values of thetatheta given csctheta=(2sqrt3)/3csctheta=(2sqrt3)/3?