Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. sin150^circ

To solve this problem, we will follow these steps:Step 1: Understand the Unit CircleThe unit circle is a circle with a radius of 1 centered at the origin (0,0) of the coordinate plane. The green dot on the positive x-axis represents a point on the unit circle, which corresponds to an angle of 0 degrees or 0 radians.Step 2: Rotate the Green Dot to the Appropriate AngleWe need to rotate the green dot to an angle of 150 degrees. Since the positive x-axis corresponds to 0 degrees, rotating the green dot 150 degrees counterclockwise will place it in the second quadrant of the coordinate plane.Step 3: Find the Coordinates of the Point at 150 DegreesOn the unit circle, each point is represented by its coordinates (x, y), which correspond to (cos(θ), sin(θ)) for an angle θ. For the angle of 150 degrees, we can use the reference angle of 30 degrees because 150 degrees is 180 degrees (a straight line) minus 30 degrees. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis.In the second quadrant, the sine of an angle is positive, while the cosine is negative. Since the sine of 30 degrees is 1/2, the sine of 150 degrees will also be 1/2. The cosine of 30 degrees is √3/2, but since we are in the second quadrant where cosine is negative, the cosine of 150 degrees will be -√3/2.Step 4: Find the Exact Value of the Sine FunctionThe exact value of the sine function for the angle 150 degrees is the y-coordinate of the point on the unit circle at that angle. As established in step 3, the sine of 150 degrees is 1/2.Answer: