range of values

[robust nexus]

i get the question and i get to solving values for cos,, but how do i know what range of values they want? it says the 5 distinct solutions but since its a cos function i could go from -pi to pi or 0 to 2pi etc,, how would i know what type of values they want ???

[drowsy talon]

sin5θ = -1/5

5θ = -0.20136,
5θ = -0.20136+2kπ
θ = -0.040272+0.4kπ , k=0,1,2,3,...

in ur calc u can just do
x=sintheta
sin(-0.040272+k(0.4pi))
and change k until u get the distinct solutions

its gonna cycle so like
from k=0 to k=4 it gives u the 5 solutions and when u try k=5 u go back to one of the roots

[robust nexus]

why cant k be less than 0 ?

also thank you thank you

[drowsy talon]

it can be but the roots cycle again