State the quadrant in which the terminal side of each angle lies
1) -55 degrees 2) -120 degrees
I'm sure you know the quadrants and their angle measurements, for positive angles.
For negative angles, start with QIV and count down to QI, moving clockwise.
To determine the quadrant in which the terminal side of each angle lies, we need to consider the signs of the angles.
1) -55 degrees:
In this case, the angle is negative (indicated by the negative sign). To find the quadrant, we can take the absolute value of the angle (ignoring the sign) and determine which quadrant the angle falls into.
Taking the absolute value of -55 degrees, we get 55 degrees.
Since 55 degrees is in the third quadrant (between 180 and 270 degrees), the terminal side of -55 degrees lies in the third quadrant.
Therefore, the answer is the third quadrant.
2) -120 degrees:
Similar to the previous example, we need to consider the sign of the angle.
In this case, the angle is also negative. Taking the absolute value of -120 degrees, we get 120 degrees.
Since 120 degrees is in the second quadrant (between 90 and 180 degrees), the terminal side of -120 degrees lies in the second quadrant.
Therefore, the answer is the second quadrant.
1) -55 degrees:
To determine the quadrant in which the terminal side of -55 degrees lies, we need to consider the standard position of angles in the Cartesian coordinate system.
In the Cartesian coordinate system, the positive x-axis is the reference side, and the angles are measured counterclockwise from the positive x-axis.
-55 degrees is measured clockwise from the positive x-axis, and since it is a negative angle, it will be reflected across the x-axis.
The terminal side of -55 degrees lies in the fourth quadrant.
Therefore, the terminal side of -55 degrees lies in the fourth quadrant.
2) -120 degrees:
To determine the quadrant in which the terminal side of -120 degrees lies, we again consider the standard position of angles in the Cartesian coordinate system.
-120 degrees is measured clockwise from the positive x-axis, and since it is a negative angle, it will be reflected across the x-axis.
The terminal side of -120 degrees lies in the second quadrant.
Therefore, the terminal side of -120 degrees lies in the second quadrant.