Evaluating cos(π/3) Using the Unit Circle and Special Angle Values in Trigonometry

cos(π/3)

To evaluate cos(π/3), we can utilize the unit circle or the values of the special angles in trigonometry

To evaluate cos(π/3), we can utilize the unit circle or the values of the special angles in trigonometry.

Using the unit circle:

1. Draw a circle with a radius of 1.
2. Since cos(θ) represents the x-coordinate of a point on the unit circle at an angle θ, we need to find the x-coordinate when θ is π/3.
3. π/3 is a special angle where the reference angle is π/6.
4. Locate the angle π/6 (30 degrees) on the unit circle.
5. The x-coordinate of the point on the unit circle at π/6 is √3/2.
6. Now since π/3 is twice the angle π/6, we know that cos(π/3) will have the same x-coordinate as cos(π/6).
7. Therefore, cos(π/3) = √3/2.

Using the values of special angles:

Another way to determine cos(π/3) is by memorizing the values of special angles.

In trigonometry, we have the following special angles and their cosine values:

– cos(0) = 1
– cos(π/6) = √3/2
– cos(π/4) = 1/√2
– cos(π/3) = 1/2
– cos(π/2) = 0

Since π/3 is one of the special angles, we know that cos(π/3) = 1/2.

Therefore, cos(π/3) can be equal to either √3/2 or 1/2, depending on the method you use to evaluate it.

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