To find a positive angle less than 2π that is coterminal with a given angle, we need to subtract or add multiples of 360° (for degrees) or 2π (for radians) until we land within the desired range.
For 425 Degrees:
1. First, we subtract 360° from 425°:
425° – 360° = 65°
2. Since 65° is less than 360° and positive, it is coterminal with 425°.
Therefore, the positive angle less than 2π that is coterminal with 425° is 65°.
For 27π/4 Radians:
1. First, we convert 2π to a fraction with a common denominator to make the calculations easier. Since 2π = 8π/4, we can subtract multiples of 2π (8π/4):
27π/4 – 8π/4 = 19π/4
2. We can subtract again since 19π/4 is still greater than 2π:
19π/4 – 8π/4 = 11π/4
3. Subtracting once more gives us:
11π/4 – 8π/4 = 3π/4
4. Now, 3π/4 is less than 2π and positive.
Thus, the positive angle less than 2π that is coterminal with 27π/4 is 3π/4.