Question

sin2 θ = 2 sin θ + 3

Answer 1

Hint:
Domain of sin(x) is [-1,1]
So
[-1,1]=2[-1,1]+3
What is the value of \(sin(\theta)\) on the right hand side to satisfy the preceding equality?
[-1,1] means the continuous interval from -1 to 1inclusively.

Answer 2

is this the equation
sin(2t ) = 2 sin(t) +3

2sin t cos t = 2 sin t + 3

Answer 3

or is it
sin^2(t) = 2 sin t + 3

Answer 4

if its the latter, you can make it a quadratic expression

sin^2(t) - 2sin (t) -3 = 0

Answer 5

and then factor

Answer 6

@mathmate
the domain of sin x is (-oo,oo) , or all real numbers

Answer 7

I think the space between the 2 and the theta that user posted should indicate
that (s)he wants, \(\large\color{black}{ \sin^2(\theta) }\) \(\LARGE\color{white}{ \rm \left| \right| }\)
So I would go with: \(\large\color{black}{ \sin^2(\theta) =2\sin(\theta)+3 }\) \(\LARGE\color{white}{ \rm \left| \right| }\)

Answer 8

@perl oops, a moment of distraction! Thanks for heads up. :)