# How do I determine which quadrant something is in?For example, if I am to evaluate cos (pi/4), how would I go about doing this? Isn't cos pi/4 postive in both quadrants 1 and 4? If something is...

How do I determine which quadrant something is in?

For example, if I am to evaluate cos (pi/4), how would I go about doing this? Isn't cos pi/4 postive in both quadrants 1 and 4? If something is positive, how do I know which quadrant it falls in? In addition, if something is negative (for example sin (-3pi/4)) I know it can't be in quadrants 1 or 2, but how do I determine which one it falls in out of the remaining quadrants?

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### 1 Answer

There is something you haven't understood here.

The points that make up the graph that represents cos x have two coordinates, the x-coordinate represents the values of x. The y-coordinate represents the values of cos x. Each point on the graph is (x, cos x). cos x for a particular value of x is either positive or negative, it cannot be both. For example cos (pi/4) is a constant that is positive. The point (pi/4, cos pi/4) lies in quadrant 1. It does not lie in quadrant 4. There is a different set of values of x for which the points (x, cos x) lie in quadrant 4.

You have to know the sets of values for which cos x is positive and the set of values for which the value of cos x is negative. Using this you can determine which quadrant the point under consideration lies in. Also, as the sine and cosine functions are periodic the set of values repeat after `2*pi` radians. For example, cos x is positive for all x such that `0<=x<=pi and (3*pi)/2 <= x <= 2*pi` and for all values of `x + n*2*pi` where x corresponds to the values given earlier and n is an integer.