Question

solve the equation. Give a general formula for all the solutions. 2 cosθ + 1 = 0

Answer 1

\[2\cos \theta+1=0\]
\[2\cos \theta= -1\]
\[\cos \theta=-\frac{ 1 }{ 2 }\]
\[\cos \theta=-\cos \frac{ \pi }{ 3 }\]
\[\cos \theta=\cos(\pi+\frac{ \pi }{ 3 })\]
\[\theta=2n \pi \pm \frac{ \pi }{ 3 }\] ...where \[n \epsilon I\]

Answer 2

The answer choice are
A.) θ=3π/2+kπ
B.) θ=2π/3+2kπ, θ=4π/3+2kπ
C.) θ=π/2+2kπ, θ=3π/2+2kπ
D.) θ=2π/3+kπ, θ=4π/3+kπ

Answer 3

hey sry I was wrong in last step
\[\theta=2n \pi+\frac{ 4\pi }{ 3 }\]..........(1)
and
\[\theta=2n \pi-\frac{ 4\pi }{ 3 }\] ........(2)
where
nϵI
now put n=k in equation 1 and n= k+1 in equation 2
you will get the answer

Answer 4

That's fine. Thank you so much ^^