Each quadrant represents a \(\displaystyle \frac{\pi }{2}\) change in radians. Therefore, an angle of \(\displaystyle \frac{-7\pi }{6}\) radians would pass through quadrants \(\displaystyle IV\), \(\displaystyle III\), and end in quadrant \(\displaystyle II\). The movement of the angle is in the clockwise direction because it is negative.

Each quadrant represents a \(\displaystyle 90^{\circ}\) change in degrees. Therefore, an angle of \(\displaystyle -380^{\circ}\) radians would pass through quadrants \(\displaystyle IV\), \(\displaystyle III\), \(\displaystyle II\), \(\displaystyle I\) and end in quadrant \(\displaystyle IV\). The movement of the angle is in the clockwise direction because it is negative.

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between \(\displaystyle 180^{\circ}\) and \(\displaystyle 270^{\circ}\), the angle is a third quadrant angle. Since \(\displaystyle 240^{\circ}\) is between \(\displaystyle 180^{\circ}\) and \(\displaystyle 270^{\circ}\), it is a thrid quadrant angle.

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than \(\displaystyle 360^{\circ}\)  we can divide the angle by \(\displaystyle 360\) and cut off the whole number part. If we divide \(\displaystyle 420^{\circ}\) by \(\displaystyle 360\), the integer part would be \(\displaystyle 1\) and the remaining is \(\displaystyle 60^{\circ}\). Now we should find the quadrant for this angle.

When the angle is between \(\displaystyle 0^{\circ}\) and \(\displaystyle 90^{\circ}\), the angle is a first quadrant angle. Since \(\displaystyle 60^{\circ}\) is between \(\displaystyle 0^{\circ}\) and \(\displaystyle 90^{\circ}\), it is a first quadrant angle.

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side.

When the angle is more than \(\displaystyle 360^{\circ}\) we can divide the angle by \(\displaystyle 360\) and cut off the whole number part. If we divide \(\displaystyle 820^{\circ}\) by \(\displaystyle 360\), the integer part would be \(\displaystyle 2\) and the remaining is \(\displaystyle 100^{\circ}\). Now we should find the quadrant for this angle.

When the angle is between \(\displaystyle 90^{\circ}\) and \(\displaystyle 180^{\circ}\), the angle is a second quadrant angle. Since \(\displaystyle 100^{\circ}\) is between \(\displaystyle 90^{\circ}\) and \(\displaystyle 180^{\circ}\), it is a second quadrant angle.

First we can convert it to degrees:

\(\displaystyle \frac{10\pi}{3}\times \frac{180^{\circ}}{\pi}=600^{\circ}\)

When the angle is more than \(\displaystyle 360^{\circ}\) we can divide the angle by \(\displaystyle 360\) and cut off the whole number part. If we divide \(\displaystyle 600^{\circ}\) by \(\displaystyle 360\), the integer part would be \(\displaystyle 1\) and the remaining is \(\displaystyle 240^{\circ}\). Now we should find the quadrant for this angle.

When the angle is between \(\displaystyle 180^{\circ}\) and \(\displaystyle 270^{\circ}\), the angle is a third quadrant angle. Since \(\displaystyle 240^{\circ}\) is between \(\displaystyle 180^{\circ}\) and \(\displaystyle 270^{\circ}\), it is a third quadrant angle.

First we can write:

\(\displaystyle \frac{3\pi}{4}\times \frac{180^{\circ}}{\pi}=135^{\circ}\)

The coordinate plane is divided into four regions, or quadrants. An angle can be located in the first, second, third and fourth quadrant, depending on which quadrant contains its terminal side. When the angle is between \(\displaystyle 90^{\circ}\) and \(\displaystyle 180^{\circ}\), the angle is a second quadrant angle. Since \(\displaystyle 135^{\circ}\) is between \(\displaystyle 90^{\circ}\) and \(\displaystyle 180^{\circ}\), it is a second quadrant angle.

When we think of angles, we go clockwise from the positive x axis.

Thus, for negative angles, we go counterclockwise. Since each quadrant is defined by 90˚, we end up in the 3rd quadrant. 

The angle 315 degrees is located in the fourth quadrant.  The correct coordinate designating this angle is \(\displaystyle (1,-1)\).

The tangent of an angle is \(\displaystyle \frac{y}{x}\).

Therefore, 

\(\displaystyle tan(315)= \frac{y}{x}= \frac{-1}{1}=-1\)