Is the angle 11pi/12 on the unit circle the same as the angle -pi/12? I'm thinking it would be, but I'm not sure.
Whoops nevermind. I was thinking if they were 11pi/6 and -pi/6.
No, they are not
11π/12 is in quadrant II
=π/12 is in IV
To determine if the angles 11π/12 and -π/12 on the unit circle are the same, we can compare their corresponding points on the unit circle.
1. Start by visualizing the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane.
2. The angle 11π/12 is a counterclockwise rotation from the positive x-axis. To find its corresponding point on the unit circle, divide 2π into twelve equal parts and move 11 steps counterclockwise.
3. To simplify 11π/12, cancel out any common factors between the numerator (11) and the denominator (12). In this case, both 11 and 12 are relatively prime, so we cannot simplify it further.
4. Divide the total angle of 2π into twelve equal parts. Each part will measure (2π)/12 = π/6. Start from the positive x-axis and count 11 parts counterclockwise, which brings us to the point on the unit circle.
5. The angle -π/12 is a clockwise rotation from the positive x-axis. To find its corresponding point on the unit circle, divide 2π into twelve equal parts and move 1 step clockwise.
6. To simplify -π/12, multiply both the numerator (-1) and the denominator (12) by -1, which gives us π/12.
7. Divide the total angle of 2π into twelve equal parts. Each part will measure (2π)/12 = π/6. Start from the positive x-axis and count 1 part clockwise, which brings us to the point on the unit circle.
8. Now, compare the two points on the unit circle obtained in step 4 and step 7. If the points coincide, then the angles 11π/12 and -π/12 are the same; otherwise, they are different.
By following these steps, you can determine if the angles 11π/12 and -π/12 on the unit circle are the same.