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Cos pi/3
The value of cos pi/3 is 0.5. Cos pi/3 radians in degrees is written as cos ((π/3) × 180°/π), i.e., cos (60°). In this article, we will discuss the methods to find the value of cos pi/3 with examples.
 Cos pi/3: 1/2
 Cos pi/3 in decimal: 0.5
 Cos (pi/3): 0.5 or 1/2
 Cos pi/3 in degrees: cos (60°)
What is the Value of Cos pi/3?
The value of cos pi/3 in decimal is 0.5. Cos pi/3 can also be expressed using the equivalent of the given angle (pi/3) in degrees (60°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/3 radians = pi/3 × (180°/pi) = 60° or 60 degrees
∴ cos pi/3 = cos π/3 = cos(60°) = 1/2 or 0.5
Explanation:
For cos pi/3, the angle pi/3 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos pi/3 value = 1/2 or 0.5
Since the cosine function is a periodic function, we can represent cos pi/3 as, cos pi/3 = cos(pi/3 + n × 2pi), n ∈ Z.
⇒ cos pi/3 = cos 7pi/3 = cos 13pi/3 , and so on.
Note: Since, cosine is an even function, the value of cos(pi/3) = cos(pi/3).
Methods to Find Value of Cos pi/3
The cosine function is positive in the 1st quadrant. The value of cos pi/3 is given as 0.5. We can find the value of cos pi/3 by:
 Using Unit Circle
 Using Trigonometric Functions
Cos pi/3 Using Unit Circle
To find the value of cos π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/3 angle with the positive xaxis.
 The cos of pi/3 equals the xcoordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cos pi/3 = x = 0.5
Cos pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos pi/3 as:
 ± √(1sin²(pi/3))
 ± 1/√(1 + tan²(pi/3))
 ± cot(pi/3)/√(1 + cot²(pi/3))
 ±√(cosec²(pi/3)  1)/cosec(pi/3)
 1/sec(pi/3)
Note: Since pi/3 lies in the 1st Quadrant, the final value of cos pi/3 will be positive.
We can use trigonometric identities to represent cos pi/3 as,
 cos(pi  pi/3) = cos 2pi/3
 cos(pi + pi/3) = cos 4pi/3
 sin(pi/2 + pi/3) = sin 5pi/6
 sin(pi/2  pi/3) = sin pi/6
☛ Also Check:
Examples Using Cos pi/3

Example 1: Using the value of cos pi/3, solve: (1sin²(pi/3)).
Solution:
We know, (1sin²(pi/3)) = (cos²(pi/3)) = 0.25
⇒ (1sin²(pi/3)) = 0.25 
Example 2: Find the value of 2 cos(pi/3)/3 sin(pi/6).
Solution:
Using trigonometric identities, we know, cos(pi/3) = sin(pi/2  pi/3) = sin pi/6.
⇒ cos(pi/3) = sin(pi/6)
⇒ Value of 2 cos(pi/3)/3 sin(pi/6) = 2/3 
Example 3: Find the value of cos pi/3 if sec pi/3 is 2.
Solution:
Since, cos pi/3 = 1/sec(pi/3)
⇒ cos pi/3 = 1/2 = 0.5
FAQs on Cos pi/3
What is Cos pi/3?
Cos pi/3 is the value of cosine trigonometric function for an angle equal to π/3 radians. The value of cos pi/3 is 1/2 or 0.5
How to Find Cos pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos pi/3 can be given in terms of other trigonometric functions as:
 ± √(1sin²(pi/3))
 ± 1/√(1 + tan²(pi/3))
 ± cot(pi/3)/√(1 + cot²(pi/3))
 ±√(cosec²(pi/3)  1)/cosec(pi/3)
 1/sec(pi/3)
☛ Also check: trigonometry table
How to Find the Value of Cos pi/3?
The value of cos pi/3 can be calculated by constructing an angle of π/3 radians with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos pi/3 is equal to the xcoordinate (0.5). ∴ cos pi/3 = 0.5.
What is the Value of Cos pi/3 in Terms of Cosec pi/3?
Since the cosine function can be represented using the cosecant function, we can write cos pi/3 as [√(cosec²(pi/3)  1)/cosec pi/3]. The value of cosec pi/3 is equal to 1.15470.
What is the Value of Cos pi/3 in Terms of Sin pi/3?
Using trigonometric identities, we can write cos pi/3 in terms of sin pi/3 as, cos(pi/3) = √(1  sin²(pi/3)). Here, the value of sin pi/3 is equal to √3/2.
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