Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
sine, 330, degrees
sin330
∘
To rotate the green dot to the appropriate angle, we start at the positive x-axis and rotate counterclockwise by 330 degrees.
To find the exact value of sine 330 degrees, we can look at the point where the green dot ends up after rotating.
In the unit circle, a rotation of 330 degrees corresponds to an angle of 30 degrees, which is in the first quadrant. In the first quadrant, the sine function is positive, so sine 30 degrees is positive.
Using the Pythagorean identity, sine squared plus cosine squared equals 1, we can find the exact value of sine 30 degrees.
cosine 30 degrees is represented by the x-coordinate of the point on the unit circle, which is 1/2. Using the Pythagorean identity, we can find sine 30 degrees:
sin^2 30 + cos^2 30 = 1
sin^2 30 + (1/2)^2 = 1
sin^2 30 + 1/4 = 1
sin^2 30 = 1 - 1/4
sin^2 30 = 3/4
sin 30 = √(3/4)
Since we're in the first quadrant and the sine function is positive, the exact value of sine 330 degrees is √(3/4).