If the angle is acute then all(sin, cos, tan) will be positive.
If it is in the second quadrant, then only sin will be positive. Hence we wrote sin as 0.5 while tan had a negative sign in front of it.
When something is in the 2nd quadrant then the angle is between 90 and 180deg, hence the angle is obtuse.
If the angle is reflex(greater than 180deg) then it will be in the 3rd or 4th quadrant. To decide it is in which quadrant we will have to look at the sign.
Example:If a question says that
cosθ=21 and
θ is reflex.
So due to reflex we know that it should be in the 3rd or 4th quadrant.
We know that only tan is positive in the 3rd quadrant while only cos is positive in the 4th quadrant.
In the question cos is positive, hence we can deduce that
θ is in the 4th quadrant.
Does it makes sense?