How do you find which quadrant each question is referring to if pi<a<3pi/2, 3pi/2<B<2pi?

1 Answer
Mar 18, 2018

While pi < a < (3pi)/2 refers to Q3, (3pi)/2 < B < 2pi refers to Q4

Explanation:

Cartesian plane is divided into four quadrants.

In first quadrant we have both abscissa and ordinates positive. In this quadrant, if we join the point to origin, the angle formed by this line with positive side of x-axis, say theta is between 0^@ and 90^@ or pi/2 (in radians), which we can write as 0 < theta < pi/2.

In second quadrant while abscissa is negative, ordinate is positive. In this quadrant, if we join the point to origin, the angle theta formed by this line with positive side of x-axis is between 90^@ and 180^@ or between pi/2 and pi, which we can write as pi/2 < theta < pi.

In third quadrant while abscissa and ordinate both are negative. In this quadrant, if we join the point to origin, the angle theta formed by this line with positive side of x-axis is between 180^@ and 270^@ or between pi and (3pi)/2, which we can write as pi < theta < (3pi)/2.

In fourth quadrant while abscissa is positive, ordinate is negative. In this quadrant, if we join the point to origin, the angle theta formed by this line with positive side of x-axis is between 270^@ and 360^@ or between (3pi)/2 and 2pi, which we can write as (3pi)/2 < theta < 2pi.
![https://www.mathsisfun.com/algebra/http://trig-four-quadrants.html](https://useruploads.socratic.org/NQLQxX0xQO6an05N2eGb_Quadrants.gif)

Hence while pi < a < (3pi)/2 refers to Q3, (3pi)/2 < B < 2pi refers to Q4