The unit circle is a circle of radius 1 centered at the origin (0, 0) on a coordinate plane. To find the terminal point corresponding to an angle of 3π/4, we need to understand how angles are represented on the unit circle.
First, the angle 3π/4 radians is equivalent to 135 degrees. This angle is located in the second quadrant of the unit circle, where the x-coordinates are negative and the y-coordinates are positive.
To find the coordinates of the terminal point, we can use the cosine and sine functions:
- x-coordinate: This is given by the cosine of the angle:
x = cos(3π/4) - y-coordinate: This is given by the sine of the angle:
y = sin(3π/4)
We know that:
cos(3π/4) = -√2/2sin(3π/4) = √2/2
So, the terminal point at the angle 3π/4 in the unit circle is:
(-√2/2, √2/2)
Thus, the coordinates of the terminal point on the unit circle determined by the angle 3π/4 are (-√2/2, √2/2).