Question

What are the values of M and theta in the diagram below

Answer 1

Answer: $B)\quad m=\dfrac{\sqrt3}{2}, \theta=\dfrac{\pi}{3}$

Step-by-step explanation:

refer to the Unit Circle. Notice that the coordinates are (cos Θ, sin Θ).  

When does sin Θ = 1/2? --------> $when\ cos\ \theta = \dfrac{\sqrt3}{2}$

This occurs at 60°  (π/3).

Answer 2

The value of m from the diagram is √3/2

To get the value of m from the given diagram, we will use the distance formula expressed as:

$r=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Given the coordinate points (0, 0) and (m, 0.5). Substitute into the formula to have:

$1=\sqrt{(m-0)^2+(0.5-0)^2} \\1 = m^2+0.5^2\\m^2 = 1-0.25\\m^2 =3/4\\m =\frac{\sqrt{3}}{2}$

Hence the value of m from the diagram is √3/2

Learn more on distance formula here: https://brainly.com/question/1872885