Answer:
To find the degree measures of all angles with cosine 1/2, we can use the unit circle, which is a circle with a radius of 1 centered at the origin of the coordinate plane. The x-coordinate of a point on the unit circle represents the cosine of the angle formed between the positive x-axis and the line segment connecting the origin to the point.
When cosine is 1/2, we know that the x-coordinate of the point on the unit circle is 1/2. We can use the Pythagorean theorem to find the y-coordinate of the point:
1^2 + y^2 = 1^2
y^2 = 1 - 1/4
y^2 = 3/4
y = ±√(3/4)
y = ±(√3)/2
So the two angles with cosine 1/2 are the angles whose terminal sides intersect the unit circle at the points (1/2, √3/2) and (1/2, -√3/2). To find these angles in degrees, we can use the inverse cosine function:
cos⁻¹(1/2) ≈ 60
cos⁻¹(1/2) + 360 ≈ 300
Therefore, the degree measures of all angles with cosine 1/2 are approximately 60° and 300°.
Step-by-step explanation: :)