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Using a unit circle, what are the degree measures of all angles with the given cosine?
1/2

User Naglerrr
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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: :)

User Dognotdog
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