no calculator is allowed on this question. given a circle with radius 1 centered at the origin, there is a…

no calculator is allowed on this question. given a circle with radius 1 centered at the origin, there is a point m where the terminal ray of the standard position angle θ intersects the circle. the coordinates of point m are (\\frac{1}{2}, \\frac{\\sqrt{3}}{2}). what is the sine of the angle θ? select one answer a \\(-\\frac{\\sqrt{3}}{2}\\) b \\(-\\frac{1}{2}\\) c \\(\\frac{1}{2}\\) d \\(\\frac{\\sqrt{3}}{2}\\)

no calculator is allowed on this question. given a circle with radius 1 centered at the origin, there is a point m where the terminal ray of the standard position angle θ intersects the circle. the coordinates of point m are (\\frac{1}{2}, \\frac{\\sqrt{3}}{2}). what is the sine of the angle θ? select one answer a \\(-\\frac{\\sqrt{3}}{2}\\) b \\(-\\frac{1}{2}\\) c \\(\\frac{1}{2}\\) d \\(\\frac{\\sqrt{3}}{2}\\)

Answer

Explanation:

Step1: Recall the unit circle definition

For a point ((x, y)) on the unit circle (radius (r = 1)) corresponding to an angle (\theta) in standard position, the sine of the angle (\theta) is given by (y)-coordinate of the point, i.e., (\sin\theta=y).

Step2: Identify the (y)-coordinate of point (M)

The coordinates of point (M) are (\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)). Here, the (y)-coordinate (y = \frac{\sqrt{3}}{2}).

Step3: Determine (\sin\theta)

Using the definition from Step 1, since (y=\frac{\sqrt{3}}{2}), we have (\sin\theta=\frac{\sqrt{3}}{2}).

Answer:

D. (\frac{\sqrt{3}}{2})