How do you evaluate #sin(-pi/6)#?
We should first convert to degrees using the conversion ratio
For the time being, disregard the negative sign.
Now, referring to our special triangles, we find that 30 degrees is part of the
The definition of sin is opposite/hypotenuse, therefore our ratio is
Imagine drawing your angle in standard position. If it was positive, you would go counter-clockwise. However, if it was negative you would draw it in a clock-wise direction. So, we can state that 30 and -30 degrees measure the same thing, it's just that they are to be drawn in different directions and different quadrants. By extension, the sides of the special triangle must measure the same thing, with one exception: your ratio will be
Hopefully this helps.