Question

Assuming that t is a real number, what is the terminal point on the unit circle for t = 3π?

a) (1, 0)
b) (-1, 0)
c) (0, 1)
d) (0, -1)

Answer 1

The terminal point on the unit circle for t = 3π is (-1, 0), which is halfway around a second rotation of the circle, putting us on the negative x-axis.

coreect option is b) (-1, 0)

Step-by-step explanation:

The terminal point on the unit circle for t = 3π can be found by understanding the circumference of the unit circle and the radian measure. The unit circle has a circumference of 2π, which means every 2π radians, we complete a full circle and are back at the starting point (1,0).

Since t = 3π is 1.5 times the full circle, this means we've gone around the circle once (2π) and half of another circle (0.5π), putting us at the negative x-axis. Therefore, the terminal point is at (-1, 0), which corresponds to answer choice b.+