Cos pi/6

The value of cos pi/6 is 0.8660254. . .. Cos pi/6 radians in degrees is written as cos ((π/6) × 180°/π), i.e., cos (30°). In this article, we will discuss the methods to find the value of cos pi/6 with examples.

• Cos pi/6: √3/2
• Cos pi/6 in decimal: 0.8660254. . .
• Cos (-pi/6): 0.8660254. . . or √3/2
• Cos pi/6 in degrees: cos (30°)

What is the Value of Cos pi/6?

The value of cos pi/6 in decimal is 0.866025403. . .. Cos pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees
∴ cos pi/6 = cos π/6 = cos(30°) = √3/2 or 0.8660254. . .

Explanation:

For cos pi/6, the angle pi/6 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos pi/6 value = √3/2 or 0.8660254. . .
Since the cosine function is a periodic function, we can represent cos pi/6 as, cos pi/6 = cos(pi/6 + n × 2pi), n ∈ Z.
⇒ cos pi/6 = cos 13pi/6 = cos 25pi/6 , and so on.
Note: Since, cosine is an even function, the value of cos(-pi/6) = cos(pi/6).

Methods to Find Value of Cos pi/6

The cosine function is positive in the 1st quadrant. The value of cos pi/6 is given as 0.86602. . .. We can find the value of cos pi/6 by:

• Using Trigonometric Functions
• Using Unit Circle

Cos pi/6 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos pi/6 as:

• ± √(1-sin²(pi/6))
• ± 1/√(1 + tan²(pi/6))
• ± cot(pi/6)/√(1 + cot²(pi/6))
• ±√(cosec²(pi/6) - 1)/cosec(pi/6)
• 1/sec(pi/6)

Note: Since pi/6 lies in the 1st Quadrant, the final value of cos pi/6 will be positive.

We can use trigonometric identities to represent cos pi/6 as,

• -cos(pi - pi/6) = -cos 5pi/6
• -cos(pi + pi/6) = -cos 7pi/6
• sin(pi/2 + pi/6) = sin 2pi/3
• sin(pi/2 - pi/6) = sin pi/3

Cos pi/6 Using Unit Circle

To find the value of cos π/6 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.
• The cos of pi/6 equals the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of cos pi/6 = x = 0.866 (approx)

☛ Also Check:

• tan 7pi/6
• sin 9pi/2
• sin 7pi
• sin 2pi
• sin 7pi/6
• sec pi/2

FAQs on Cos pi/6

What is Cos pi/6?

Cos pi/6 is the value of cosine trigonometric function for an angle equal to π/6 radians. The value of cos pi/6 is √3/2 or 0.866 (approx)

What is the Value of Cos pi/6 in Terms of Sin pi/6?

Using trigonometric identities, we can write cos pi/6 in terms of sin pi/6 as, cos(pi/6) = √(1 - sin²(pi/6)). Here, the value of sin pi/6 is equal to 1/2.

How to Find Cos pi/6 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos pi/6 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(pi/6))
• ± 1/√(1 + tan²(pi/6))
• ± cot(pi/6)/√(1 + cot²(pi/6))
• ±√(cosec²(pi/6) - 1)/cosec(pi/6)
• 1/sec(pi/6)

☛ Also check: trigonometry table

What is the Exact Value of cos pi/6?

The exact value of cos pi/6 can be given accurately up to 8 decimal places as 0.86602540 and √3/2 in fraction.

How to Find the Value of Cos pi/6?

The value of cos pi/6 can be calculated by constructing an angle of π/6 radians with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos pi/6 is equal to the x-coordinate (0.866). ∴ cos pi/6 = 0.866.