2x is a 2nd quadrant angle. In which quadrant does x/2 lie?
or
2x is a 2nd quadrant angle :
--> 90° < 2x < 180°
22.5° < x/2 < 45° , which is in quadrant I
To determine in which quadrant x/2 lies, we first need to identify the quadrant where 2x lies. Since 2x is a second quadrant angle, it means that it falls between 90 degrees and 180 degrees on the unit circle.
To find the quadrant where x/2 lies, we need to divide 2x by 2.
x/2 = (2x)/2 = x
Since x/2 is equal to x, it means that x/2 also lies in the second quadrant. Thus, x/2 lies in the second quadrant.
To determine the quadrant in which x/2 lies, we need to consider the signs of x and 2.
Given that 2x is a second quadrant angle, we know that it lies between 90 degrees and 180 degrees. The second quadrant consists of angles where the x-coordinate is negative, and the y-coordinate is positive.
Now, let's consider x/2. To find its quadrant, we need to divide x by 2. If x is positive, the quotient will also be positive, and if x is negative, the quotient will be negative.
Since 2x is in the second quadrant and has a negative x-coordinate, we can deduce that x is negative. Therefore, when we divide a negative x by 2, the quotient will also be negative.
A negative quotient indicates that x/2 is in the fourth quadrant. In the fourth quadrant, both the x-coordinate and the y-coordinate are negative.
So, x/2 lies in the fourth quadrant.
The maximum 2x can be is 179.99999, so half of that is in the first quadrant., and half that is in the first quadrant. So it usually is.
But what if x is 460 degrees, in the second quadrant? Hmmm, well, then half is 230, or the third quadrant, and half that is in second quadrant. So if 2x is less than 179.99999, then the answer is as in the first paragraph.