Name the quadrant that contains each angle
a.) 2pi/3
b.) 230 degrees
c.) pi/6
d.) 120 degrees
e.) 7pi/4
for degrees, the boundaries are at 0,90,180,270,360
for radians, that is 0,pi/2,p,3pi/2,2pi
Assuming you can work with fractions, there should be no problem. What are your responses?
gfigiigi
To determine the quadrant that contains each angle, we need to understand the relationship between angles and quadrants on the Cartesian coordinate plane.
First, let's briefly discuss the quadrants:
- The first quadrant (Q1) is located in the upper right section of the plane.
- The second quadrant (Q2) is in the upper left section.
- The third quadrant (Q3) is in the lower left section.
- The fourth quadrant (Q4) is in the lower right section.
Now, let's identify the quadrant for each angle:
a.) 2π/3:
This angle is greater than 180 degrees but less than 270 degrees. Therefore, it lies in the third quadrant (Q3).
b.) 230 degrees:
To convert this degree measure to radians, we need to multiply by π/180:
230 * π/180 = 23π/18.
This angle is greater than 180 degrees but less than 270 degrees, so it also falls into the third quadrant (Q3).
c.) π/6:
This angle is less than 90 degrees, so it is located in the first quadrant (Q1).
d.) 120 degrees:
To convert this degree measure to radians, we multiply by π/180:
120 * π/180 = 2π/3.
This angle is greater than 90 degrees but less than 180 degrees, so it is situated in the second quadrant (Q2).
e.) 7π/4:
This angle is greater than 270 degrees but less than 360 degrees. So, it falls into the fourth quadrant (Q4).
In summary:
a.) 2π/3 is in the third quadrant (Q3).
b.) 230 degrees is also in the third quadrant (Q3).
c.) π/6 is in the first quadrant (Q1).
d.) 120 degrees is in the second quadrant (Q2).
e.) 7π/4 is in the fourth quadrant (Q4).