what is the reference angle for 17 pi/12?
17π/12 is in III
so reference angle = 17π/12 - π = 5π/12
To find the reference angle for an angle given in radians, you can follow these steps:
Step 1: Convert the angle to its equivalent positive acute angle.
In this case, we have 17π/12. To convert it to a positive acute angle, we need to subtract the nearest multiple of 2π (one full revolution), essentially bringing the angle within the first revolution.
Since 2π is equal to 12π/6, we can subtract 12π/6 from 17π/12:
17π/12 - 12π/6 = (17π - 24π)/12 = -7π/12
Step 2: Determine the positive acute angle by taking the absolute value.
Since we need the positive acute angle, we take the absolute value of -7π/12:
| -7π/12 | = 7π/12
So, the positive acute angle is 7π/12.
Therefore, the reference angle for 17π/12 is 7π/12.
To find the reference angle for an angle measured in radians, follow these steps:
1. Convert the angle from radians to degrees.
- In this case, the angle is 17π/12. To convert it to degrees, multiply by 180/π.
(17π/12) * (180/π) = (17 * 180) / (12) = 255/2 = 127.5 degrees
2. Find the reference angle.
- The reference angle is the acute angle between the terminal side of the given angle and the x-axis in standard position.
- Since the angle is measured counterclockwise, we subtract the angle from 180 degrees.
Reference angle = 180 - 127.5 = 52.5 degrees
3. Convert the reference angle back to radians.
- To express the reference angle in radians, multiply the reference angle in degrees by π/180.
Reference angle = 52.5 * π/180 = 7π/24
Therefore, the reference angle for 17π/12 is 7π/24.