Cos 5pi/3
The value of cos 5pi/3 is 0.5. Cos 5pi/3 radians in degrees is written as cos ((5π/3) × 180°/π), i.e., cos (300°). In this article, we will discuss the methods to find the value of cos 5pi/3 with examples.
 Cos 5pi/3: 1/2
 Cos 5pi/3 in decimal: 0.5
 Cos (5pi/3): 0.5 or 1/2
 Cos 5pi/3 in degrees: cos (300°)
What is the Value of Cos 5pi/3?
The value of cos 5pi/3 in decimal is 0.5. Cos 5pi/3 can also be expressed using the equivalent of the given angle (5pi/3) in degrees (300°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 5pi/3 radians = 5pi/3 × (180°/pi) = 300° or 300 degrees
∴ cos 5pi/3 = cos 5π/3 = cos(300°) = 1/2 or 0.5
Explanation:
For cos 5pi/3, the angle 5pi/3 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 5pi/3 value = 1/2 or 0.5
Since the cosine function is a periodic function, we can represent cos 5pi/3 as, cos 5pi/3 = cos(5pi/3 + n × 2pi), n ∈ Z.
⇒ cos 5pi/3 = cos 11pi/3 = cos 17pi/3 , and so on.
Note: Since, cosine is an even function, the value of cos(5pi/3) = cos(5pi/3).
Methods to Find Value of Cos 5pi/3
The cosine function is positive in the 4th quadrant. The value of cos 5pi/3 is given as 0.5. We can find the value of cos 5pi/3 by:
 Using Trigonometric Functions
 Using Unit Circle
Cos 5pi/3 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 5pi/3 as:
 ± √(1sin²(5pi/3))
 ± 1/√(1 + tan²(5pi/3))
 ± cot(5pi/3)/√(1 + cot²(5pi/3))
 ±√(cosec²(5pi/3)  1)/cosec(5pi/3)
 1/sec(5pi/3)
Note: Since 5pi/3 lies in the 4th Quadrant, the final value of cos 5pi/3 will be positive.
We can use trigonometric identities to represent cos 5pi/3 as,
 cos(pi  5pi/3) = cos(2pi/3)
 cos(pi + 5pi/3) = cos 8pi/3
 sin(pi/2 + 5pi/3) = sin 13pi/6
 sin(pi/2  5pi/3) = sin(7pi/6)
Cos 5pi/3 Using Unit Circle
To find the value of cos 5π/3 using the unit circle:
 Rotate ‘r’ anticlockwise to form 5pi/3 angle with the positive xaxis.
 The cos of 5pi/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 5pi/3 = x = 0.5
☛ Also Check:
Examples Using Cos 5pi/3

Example 1: Find the value of 2 cos(5pi/3)/3 sin(7pi/6).
Solution:
Using trigonometric identities, we know, cos(5pi/3) = sin(pi/2  5pi/3) = sin(7pi/6).
⇒ cos(5pi/3) = sin(7pi/6)
⇒ Value of 2 cos(5pi/3)/3 sin(7pi/6) = 2/3 
Example 2: Find the value of (cos² 5pi/6  sin² 5pi/6). [Hint: Use cos 5pi/3 = 0.5]
Solution:
Using the cos 2a formula,
(cos² 5pi/6  sin² 5pi/6) = cos(2 × 5pi/6) = cos 5pi/3
∵ cos 5pi/3 = 0.5
⇒ (cos² 5pi/6  sin² 5pi/6) = 0.5 
Example 3: Simplify: 8 (cos(5pi/3)/sin(13pi/6))
Solution:
We know cos 5pi/3 = sin 13pi/6
⇒ 8 cos(5pi/3)/sin(13pi/6) = 8 (cos(5pi/3)/cos(5pi/3))
= 8(1) = 8
FAQs on Cos 5pi/3
What is Cos 5pi/3?
Cos 5pi/3 is the value of cosine trigonometric function for an angle equal to 5π/3 radians. The value of cos 5pi/3 is 1/2 or 0.5
How to Find Cos 5pi/3 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 5pi/3 can be given in terms of other trigonometric functions as:
 ± √(1sin²(5pi/3))
 ± 1/√(1 + tan²(5pi/3))
 ± cot(5pi/3)/√(1 + cot²(5pi/3))
 ±√(cosec²(5pi/3)  1)/cosec(5pi/3)
 1/sec(5pi/3)
☛ Also check: trigonometric table
What is the Value of Cos 5pi/3 in Terms of Sec 5pi/3?
Since the secant function is the reciprocal of the cosine function, we can write cos 5pi/3 as 1/sec(5pi/3). The value of sec 5pi/3 is equal to 2.
What is the Value of Cos 5pi/3 in Terms of Cot 5pi/3?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 5pi/3 can be written as cot(5pi/3)/√(1 + cot²(5pi/3)). Here, the value of cot 5pi/3 is equal to 0.57735.
How to Find the Value of Cos 5pi/3?
The value of cos 5pi/3 can be calculated by constructing an angle of 5π/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 5pi/3 is equal to the xcoordinate (0.5). ∴ cos 5pi/3 = 0.5.
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