To find angles that are coterminal with a given angle, we can add or subtract full rotations, which correspond to multiples of 2π radians. The given angle is 3π/4.
Finding Positive Coterminal Angles:
1. The first positive coterminal angle can be found by adding 2π:
3π/4 + 2π = 3π/4 + 8π/4 = 11π/4
2. The second positive coterminal angle can be found by adding another 2π:
3π/4 + 4π = 3π/4 + 16π/4 = 19π/4
Finding Negative Coterminal Angles:
1. The first negative coterminal angle can be found by subtracting 2π:
3π/4 – 2π = 3π/4 – 8π/4 = -5π/4
2. The second negative coterminal angle can be found by subtracting another 2π:
3π/4 – 4π = 3π/4 – 16π/4 = -13π/4
So, the two positive coterminal angles are 11π/4 and 19π/4, while the two negative coterminal angles are -5π/4 and -13π/4.