Explain how to find the reference angle for 1,406 degrees. Find the reference angle.
To find the reference angle for 1,406 degrees, we need to subtract the nearest multiple of 360 degrees from the given angle.
First, we find the nearest multiple of 360 degrees below 1,406:
1,406 ÷ 360 ≈ 3.905 (rounded to three decimal places)
This means that 3.905 multiples of 360 degrees lie in the range below 1,406 degrees.
Next, we subtract the product of 3.905 and 360 from 1,406:
1,406 - (3.905 × 360) ≈ 1,406 - 1,402.8 ≈ 3.2 degrees
The reference angle for 1,406 degrees is approximately 3.2 degrees.