Determine whether the angles are coterminal 3pi/4 and 29pi/4

Answer 1

To determine whether two angles are coterminal, we need to see if they end in the same position after completing one or more full revolutions around the circle.

Angle 3π/4:
One full revolution is equal to 2π radians. Therefore, 3π/4 is equivalent to 11π/4 after completing one full revolution.

Angle 29π/4:
To simplify the angle, we can divide both the numerator and denominator by 4:
29π/4 = 7(4π/4) + π/4 = 7π + π/4.

Here, we see that angle 29π/4 can be broken down into a multiple of 2π plus π/4. This tells us that it also completes one full revolution and ends in the same position as angle 3π/4.

Therefore, the angles 3π/4 and 29π/4 are coterminal.