Find the reference angle for each given angle:
a) 325 degrees
b) 14pi/3
c) -190 degrees
360 - 325 =
14/3 = 4 2/3 twice around and 2 pi/3
2 pi/3 = 120 = 180 - 60 so 60 in Q2
10 in Q2
To find the reference angle for each given angle, follow these steps:
a) 325 degrees:
- Start by subtracting 360 degrees from the given angle until you get a positive angle less than 360 degrees.
325 degrees - 360 degrees = -35 degrees (negative angle)
- Since the reference angle is always positive, we need to find the positive equivalent angle of -35 degrees.
- Add 360 degrees to the negative angle to get the positive equivalent:
-35 degrees + 360 degrees = 325 degrees
- The reference angle for 325 degrees is 35 degrees.
b) 14π/3 (radians):
- Convert the radian measure to degrees by using the fact that π radians is equal to 180 degrees.
14π/3 * (180 degrees/π radians) = 840 degrees/3 = 280 degrees
- The reference angle for 14π/3 radians is 280 degrees.
c) -190 degrees:
- Similar to the first step, subtract 360 degrees from the given angle until you get a positive angle less than 360 degrees.
-190 degrees - 360 degrees = -550 degrees (negative angle)
- Add 360 degrees to the negative angle to get the positive equivalent:
-550 degrees + 360 degrees = -190 degrees
- The reference angle for -190 degrees is 190 degrees.
In summary, the reference angles are:
a) 35 degrees
b) 280 degrees
c) 190 degrees