227k views
2 votes
Using the special triangle shown on the unit circle, what is the cosine of π/3?

(a) ²∕₂
(b) ½
(c) √₃∕₂
(d) √₂∕₂

User Mehmet
by
8.7k points

1 Answer

4 votes

Final answer:

Using the 30-60-90 special right triangle on the unit circle, the cosine of π/3 is 1/2, corresponding to the length of the side adjacent to the 60-degree angle.

correct option is (b) ½

Step-by-step explanation:

Using the special triangle on the unit circle, the cosine of π/3 can be determined. For an angle of π/3, which corresponds to 60 degrees, the associated point on the unit circle has an x-coordinate representing the cosine of that angle. In a 30-60-90 special right triangle, the sides are in the ratio 1:√3:2.

The shorter leg (opposite the 30-degree angle) is half the hypotenuse, and the longer leg (adjacent to the 60-degree angle) is √3 times the shorter leg. Since the hypotenuse of such a triangle on the unit circle is 1 (the radius of the unit circle), the adjacent side to the 60-degree angle, which is the cosine of π/3, is ½.

User Greig Fotheringham
by
8.5k points