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 x-axis.
• The cos of pi/3 equals the x-coordinate(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:

• ± √(1-sin²(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:

• sec 3pi
• cos 13pi/6
• sec pi
• sin 11pi/6
• cos 5pi/3
• sin pi/3

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:

• ± √(1-sin²(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 x-axis, 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 x-coordinate (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.