## New Topics

A rectangular coordinate system consists of x-axis and y-axis that divide a plane into four regions called quadrants. The point where the two axis intersect is called origin and is denoted by O.

Quadrants are usually denoted by roman letters I, II, III and IV as shown in the figure below:

• Angles between 0^\circ and 90^\circ are in the first quadrant.
• Angles between 90^\circ and 180^\circ are in the second quadrant.
• Angles between 180^\circ and 270^\circ are in the third quadrant.
• Angles between 270^\circ and 360^\circ are in the fourth quadrant.

An angle in standard position is said to lie in a quadrant if its terminal side lies in that quadrant. In the figures below, \apha lies in the 1st quadrant, \beta lies in the 2nd quadrant, \gamma lies in the 3rd quadrant and \theta lies in the 4th quadrant.

An angle in standard position is called a quadrantal angle if its terminal side lies on x-axis or y-axis. Quadrantal angles include 0^\circ, \pm90^\circ, \pm180^\circ, \pm270^\circ, \pm360^\circ etc.

Some of these angles have been illustrated in the figures below. Note that the terminal side of these angles lies either on x-axis or on y-axis.

##### Example 1:

Indicate the quadrant of each of the following angles:

1. 320^\circ
2. - 135^\circ
3. (7\pi )/ 4 radian
4. \pi radian

## Solution:

Since 320^\circ lies between 270^\circ and 360^\circ, the angle lies in the 4th quadrant.

Since -135^\circ is coterminal with -135^\circ + 360^\circ = 225^\circ and 180^\circ <225^\circ <270^\circ, therefore 225^\circ lies in the 3rd quadrant and so does -135^\circ(Coterminal angles have same terminal side)

Since (7\pi)/4 radian = 315^\circ , it lies in the 4th quadrant.

Since \pi = 180^\circ lies on x-axis, it is a quadrantal angle as shown below.

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