Alright, so I'm told to solve each equation on the interval [0, 2pi]
2(sin^2)(theta)-sin(theta)-1=0
Here is what I have done:
Factor out Sin(theta)
Sin(theta)[2(sin(theta))+1]=0
Set each part equal to zero:
Sin(theta)=0 2sin(theta)+1=0
Theta=(Pi), (2Pi) Theta=(7Pi/6), (11Pi/6)
So the solution set would be: {Theta|Theta=(Pi),(2Pi), (4Pi/3), (5Pi/3)}
However, the solutions manual says that the solution set is actually {Theta|Theta=(Pi/2),(7Pi/6),(11Pi/6)}
How do they get that Sin(Theta)=0 means that Theta=(Pi/2)? Because Sin=0 at Pi and 2Pi on the unit circle, which is what I'm working with.
Thanks for taking a look!
2(sin^2)(theta)-sin(theta)-1=0
Here is what I have done:
Factor out Sin(theta)
Sin(theta)[2(sin(theta))+1]=0
Set each part equal to zero:
Sin(theta)=0 2sin(theta)+1=0
Theta=(Pi), (2Pi) Theta=(7Pi/6), (11Pi/6)
So the solution set would be: {Theta|Theta=(Pi),(2Pi), (4Pi/3), (5Pi/3)}
However, the solutions manual says that the solution set is actually {Theta|Theta=(Pi/2),(7Pi/6),(11Pi/6)}
How do they get that Sin(Theta)=0 means that Theta=(Pi/2)? Because Sin=0 at Pi and 2Pi on the unit circle, which is what I'm working with.
Thanks for taking a look!