where does the terminal side of theta=589 degrees lay.?
To determine where the terminal side of an angle lies, we need to find the reference angle by converting the given angle to an angle between 0 and 360 degrees.
To convert 589 degrees to an equivalent angle between 0 and 360 degrees, we can subtract multiples of 360 until we have an angle in that range.
589 degrees - (1 * 360 degrees) = 229 degrees
Therefore, the reference angle of 589 degrees is 229 degrees.
Now, we need to determine where the terminal side of the angle with 229 degrees lies. In trigonometry, angles are measured counterclockwise from the positive x-axis in the standard position.
The terminal side of 229 degrees lies in the third quadrant, which is between 180 and 270 degrees.