using the unit circle, calculate the value of sin240°
To calculate the value of sin240° using the unit circle, follow these steps:
1. Start by drawing a unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0,0) in a coordinate plane.
2. Locate the angle 240° on the unit circle. Since 240° is in the third quadrant, the terminal side of the angle will be in the lower left quadrant.
3. Draw a straight line from the center of the unit circle to the terminal side of the angle. This line represents the radius of the unit circle.
4. Find the point where the line intersects the unit circle. Let's call this point A.
5. Locate the y-coordinate of point A. The y-coordinate of a point on the unit circle represents the value of sin(angle).
6. For point A, the y-coordinate is the negative square root of 3 divided by 2 since we are in the third quadrant and the y-coordinate is negative.
7. Therefore, sin240° = -√3/2 or approximately -0.866.