Question

In the diagram below, tangent theta = startroot 3 endroot. what is the value of m? a unit circle is shown. a radius with length 1 goes to point (one-half, m) on the edge of the circle and forms an angle with measure theta. startfraction startroot 3 endroot over 3 endfraction startfraction startroot 3 endroot over 2 endfraction startroot 3 endroot 2 startroot 3 endroot

Answer 1

The value of m is √3/2, which is the value of the sine of theta in a unit circle where the tangent of angle theta is √3 and the x-coordinate is 1/2.

Step-by-step explanation:

The question asks to find the value of m in a unit circle where the tangent of angle theta is √3. Since the unit circle has a radius of 1, the coordinates of a point on the circle can be expressed as (cos(theta), sin(theta)). Given that tangent theta = √3, we know from the definition of tangent that tan(theta) = sin(theta)/cos(theta). Using the provided coordinate (1/2, m) and knowing that this represents (cos(theta), sin(theta)), we can infer that cos(theta) = 1/2.

Therefore, sin(theta) = tan(theta) × cos(theta) = √3 × (1/2). Simplifying this expression gives us sin(theta) = √3/2, which means that m, representing the y-coordinate or the sine of theta, is √3/2.