Question

Solve on the interval [0,2pi): 3 csc x - 1 = 2

Answer 1

so on simplification you get 3 cosec(x) = 3

Answer 2

And further simplification you get cosec (x) = 1

Answer 3

on the interval [0,2pi) would that be 2pi/3,4pi/3?

Answer 4

\(\bf 3 csc(x) - 1 = 2\implies csc(x)=1\\ \quad \\
\textit{recall that }\qquad csc(\theta)=\cfrac{1}{sin(\theta)}\\ \quad \\

csc(x)=1\implies \cfrac{1}{sin(x)} =1 \implies \cfrac{1}{1}=sin(x)=1\\ \quad \\
sin^{-1}(1) = sin^{-1}(sin(x))\implies sin^{-1}(1) = x\)

Answer 5

now you'd just need to find those angles whose sine is 1

Answer 6

ok thanks! it all makes sense now pi/2
because sin=y