Question

Find the solutions of the equation that are in the interval [0, 2π).

2-2sin(t)=2sqrt3 * cos(t)

I would like to know how to do the work for this since it is important I learn it for my midterm next week.
As far as I can simplify it is:
1-sin(t)=sqrt3 * cos(t)

but I have no idea what I'm doing at that point.

Answer 1

Here is a better view of the equation
\[2-2\sin(t)=2\sqrt{3}\cos(t)\]

Answer 2

1-sin(t)=sqrt3 cos(t)
1+sqr(sin(t))-2sin(t)=3sqr(cos(t))
4sqr(sin(t))-2sin(t)-2=0
using quadratic eqn formula we have sin(t)=1,-1/2
checking in given eqn because while squaring root may be added we have
sin(t)=-1/2&& thus cos(t)=(sqrt3)/2
t=330degree

Answer 3

Thanks, but that makes no sense. Please, when you explain, EXPLAIN! For the most part, people may have basic knowledge of what they are asking, but they need to see the full steps to understand how the equations are manipulated. If you skip steps, magically introduce subsitutions, and other algebraic manipulations, without explaining things, then it leaves people like myself extremely confused.

Answer 4

Not to mention there are two solutions in this equation and you have only supplied one. Is the other non-existent or not?