# Sin, cos, tan, csc, sec, cot

1. Sep 15, 2004

### sfeld

I dont understand how they figure these problems out.

Give the quadrant in which each of the following points are located, and determine which of the functions are postive and which are negative.

(4, 3) Quadrant I; SIN +; COS +; TAN +; CSC +; SEC +; COT +;
I understand that I think, but how do they determine (-3,4)? Can someone explain?

2. Sep 15, 2004

### NateTG

It's not at all clear that this is the case, but my best guess is that want to know whether each of the trig functions is positive or negative if it were applied to the angle formed by the positive x axis vector from the origin to the reference point.

3. Sep 15, 2004

### HallsofIvy

Staff Emeritus
If the "point" is (x,y) (as in (-3, 4)) then cos always has the sign of the x-component, sin always has the sign of the y-component. signs of tan, cot, sec, csc, follow from their expression in terms of sign and cos.

In this example sin(&theta;) is positive (in fact, it is 4/5), cos(&theta;) is negative (it is -3/5), tan(&theta;)= sin(&theta;)/cos(&theta;)= y/x= -4/3, cot(&theta;)= cos(&theta)/&sin(theta)= -3/4, sec(&theta;)= 1/cos(&theta)= -5/3, and csc(&theta;)= 1/sin(&theta)= 5/4.
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