What are the angles in terms of π radians from 0 to 2π that have a cosine of √3/2?

What are the angles in terms of π radians from 0 to 2π that have a cosine of √3/2?

• A. π/2, 3π/2
• B. π/6, 11π/6
• C. π/4, 5π/4
• D. π/3, 5π/3

Answer: (B)

The cosine function is positive in both the first and fourth quadrants. Specifically, the cosine of an angle is equal to √3/2 at specific angles. In the first quadrant, the angle that corresponds to cos(θ) = √3/2 is π/6. This is a well-known angle in the unit circle, where the cosine of the angle represents the length of the adjacent side over the hypotenuse in a right triangle. In the fourth quadrant, the same cosine value appears again. The corresponding angle is found by subtracting π/6 from 2π (which gives a full rotation) to find the angle at this point. This calculation gives us 11π/6. Thus, the two angles between 0 and 2π where the cosine is √3/2 are accurately represented by π/6 and 11π/6. These angles meet the condition specified in the question regarding their cosine value. Other choices do not match the required cosine value of √3/2.

The cosine function is positive in both the first and fourth quadrants. Specifically, the cosine of an angle is equal to √3/2 at specific angles.

In the first quadrant, the angle that corresponds to cos(θ) = √3/2 is π/6. This is a well-known angle in the unit circle, where the cosine of the angle represents the length of the adjacent side over the hypotenuse in a right triangle.

In the fourth quadrant, the same cosine value appears again. The corresponding angle is found by subtracting π/6 from 2π (which gives a full rotation) to find the angle at this point. This calculation gives us 11π/6.

Thus, the two angles between 0 and 2π where the cosine is √3/2 are accurately represented by π/6 and 11π/6. These angles meet the condition specified in the question regarding their cosine value.

Other choices do not match the required cosine value of √3/2.