Question

The angle between 0 and 2π in radians that is coterminal with the angle
19/4π in radians is

Answer 1

The coterminal angle with 19/4π radians that lies between 0 and 2π radians is 7π/4 radians. This is found by subtracting multiples of 2π from 19/4π until the result is in the desired range.

Step-by-step explanation:

The angle between 0 and 2π in radians that is coterminal with the angle 19/4π in radians can be found by subtracting or adding multiples of 2π until the result is between 0 and 2π. Since 19/4 is larger than 2π, we will subtract multiples of 2π (4π/4) from 19π/4:

19π/4 - 4π/4 = 15π/4

Now, subtract 4π (16π/4) from 15π/4:

15π/4 - 16π/4 = -π/4

Since it is negative, we add back 8π/4 (2π) to get the angle in the desired range:

-π/4 + 8π/4 = 7π/4

The angle that is coterminal with 19/4π and is also between 0 and 2π, is 7π/4 radians.

Answer 2

(19/4)π = 4.75π

So we have to keep subtract 2π

4.75π - 2π = 2.75π

This is still more than 2π, so we subtract 2π again.

2.75π - 2π = 0.75π

So the coterminal angle = 0.75π = (3/4)π radians.