can a reference angle be negative?

Tye "reference angle" in google and check out the mathwords site :)

no

I copied and pasted the mathwords page for you, unfortunatly the diagram that was with it cant, express itself in text so it didn't appear.

For any given angle, its reference angle is an acute version of that angle. In standard position, the reference angle is the smallest angle between the terminal side and the x-axis. The values of the trig functions of angle θ are the same as the trig values of the reference angle for θ, give or take a minus sign.

no?

Yes, a reference angle can be negative.

To understand this, we need to review what a reference angle is. A reference angle is an acute angle formed between the terminal side of an angle and the x-axis in standard position. The reference angle is always positive, as it represents the smallest angle formed.

However, when determining the trigonometric functions of an angle, the signs of those functions depend on the quadrant that the angle is in. In the first and fourth quadrant, the trig functions are positive, while in the second and third quadrant, they are negative.

So, even though the reference angle itself is always positive, the trigonometric functions may have negative values depending on the quadrant. Therefore, a negative angle can have a negative reference angle, but the reference angle itself will still be positive.