The Signs of Trigonometric Functions in Quadrant I and II

[sfeld]

I don't 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 positive 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?

 

[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.

 

[HallsofIvy]

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