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

Answer:

The correct answer is m=$\frac{\sqrt{3} }{2}$ and θ = 30º.

Step-by-step explanation:

First, we must form a triangle whose hypotenuse is the radius r=1, its adjacent leg is m, its opposite leg is $\frac{1}{2}$ and the angle is theta.

First, we calculate the angle with theta's breast:

sin (θ) = $\frac{\frac{1}{2} }{H}$

where H is the hypotenuse, in this case, the radio.

θ = $sin^{-1}$ ($\frac{\frac{1}{2} }{1}$)

θ = 30º

Now, we calculate the adjacent leg, which is equal to the x-coordinate of the point:

cos (θ) = $\frac{m}{H}$

m = cos 30º * H

m = $\frac{\frac{\sqrt{3} }{2} }{1}$

m = $\frac{\sqrt{3} }{2}$

Have a nice day!