I'm trying to find out which quadrant some trigonometric functions lie in. The problem is one of them is equal to zero, and zero is neither positive or negative. How do I determine which quadrant it belongs in then???
I suggest that you "memorize" the shape and graph of the sine, cosine and tangent functions.
That way you can tell where the angle ß in such equations as sinß = 0 is.
You are correct to notice that those angles do not lie in a particular quadrants, so they are considered special cases.
e.g. sin 180º = 0
while sin 179º is positive
and sin 181º is negative.
We would have not problem deciding where 179 and 181 lie, would we?
To determine which quadrant a trigonometric function lies in when it equals zero, you need to consider the signs of the functions in each quadrant.
The quadrants of a coordinate system are divided as follows:
1st Quadrant: Positive x, Positive y
2nd Quadrant: Negative x, Positive y
3rd Quadrant: Negative x, Negative y
4th Quadrant: Positive x, Negative y
For trigonometric functions, the signs of the functions in each quadrant are as follows:
- Sine (sin): Positive in the 1st and 2nd quadrants, zero at the x-axis (positive y-axis) and negative in the 3rd and 4th quadrants.
- Cosine (cos): Positive in the 1st and 4th quadrants, zero at the y-axis (positive x-axis) and negative in the 2nd and 3rd quadrants.
- Tangent (tan): Positive in the 1st and 3rd quadrants, zero at the x-axis (positive y-axis) and negative in the 2nd and 4th quadrants.
Since zero is neither positive nor negative, it lies on the x-axis or y-axis but does not belong to any specific quadrant. When a trigonometric function equals zero, it intersects the corresponding axis without crossing into a quadrant.
Therefore, if a trigonometric function is equal to zero, it does not belong to any specific quadrant. Instead, it has points on the coordinate axes.