Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
sine, 120, degrees
sin120
∘
To find the sine of 120 degrees, we first need to rotate the green dot on the unit circle to the appropriate angle.
The angle 120 degrees is in the second quadrant, which means it is between 90 degrees and 180 degrees counterclockwise from the positive x-axis.
To find the exact angle, we can subtract 120 degrees from 180 degrees: 180 degrees - 120 degrees = 60 degrees.
So, we need to rotate the green dot to the angle of 60 degrees on the unit circle.
Now, we can find the exact value of the sine function at that angle.
Looking at the unit circle, we see that the y-coordinate of the point where the green dot is located is equal to the sine of the angle.
At 60 degrees, the y-coordinate is equal to √3/2.
Therefore, sin(120 degrees) = sin(60 degrees) = √3/2.