4cosBeta=1+2cosBeta
2cosBeta=1
cosBeta=1/2
60 degrees +/- 180--is this right?
I know there should be another answer, but I'm not sure if it needs to be 240 +/-180 or 120 +/- 180. I don't know how to tell if it's added to 180 or subtracted, could you please explain??
Why do you have +/- 180?
As to your other answer, where else is cos(Beta) = (1/2)? That will be the base of your 2nd answer. Hint: 4th quadrant.
330 degrees?
To find the possible values of β in the equation 4cosβ = 1 + 2cosβ, you have correctly simplified it to 2cosβ = 1. Next, you divided both sides by 2, resulting in cosβ = 1/2.
To determine the possible values of β, we need to look at the unit circle. The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is used to define the values of trigonometric functions for different angles.
In the unit circle, the x-coordinate represents the cosine value for a given angle. For example, when the angle is 0 degrees, the x-coordinate is 1, and when the angle is 180 degrees, the x-coordinate is -1.
Since cosβ = 1/2, we are looking for the angles where the x-coordinate is equal to 1/2. On the unit circle, this occurs at two angles: 60 degrees (1/2) and 300 degrees (-1/2).
To determine the other possible values, we need to consider the periodic nature of the cosine function. The cosine function repeats its values every 360 degrees. This means that if cosβ = 1/2 at 60 degrees, it will also be equal to 1/2 at 60 degrees + 360 degrees, 720 degrees, and so on.
To find the other angles, we add or subtract multiples of 360 degrees to the initial value of 60 degrees. Adding 360 gives us 420 degrees, 780 degrees, and so on. Subtracting 360 gives us -300 degrees, -660 degrees, and so on.
Therefore, the possible values for β are 60 degrees, 420 degrees, -300 degrees, and -660 degrees.