Cos 11pi/12

The value of cos 11pi/12 is -0.9659258. . .. Cos 11pi/12 radians in degrees is written as cos ((11π/12) × 180°/π), i.e., cos (165°). In this article, we will discuss the methods to find the value of cos 11pi/12 with examples.

• Cos 11pi/12: -(√6+√2)/4
• Cos 11pi/12 in decimal: -0.9659258. . .
• Cos (-11pi/12): -0.9659258. . . or -(√6+√2)/4
• Cos 11pi/12 in degrees: cos (165°)

What is the Value of Cos 11pi/12?

The value of cos 11pi/12 in decimal is -0.965925826. . .. Cos 11pi/12 can also be expressed using the equivalent of the given angle (11pi/12) in degrees (165°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/12 radians = 11pi/12 × (180°/pi) = 165° or 165 degrees
∴ cos 11pi/12 = cos 11π/12 = cos(165°) = -(√6+√2)/4 or -0.9659258. . .

Explanation:

For cos 11pi/12, the angle 11pi/12 lies between pi/2 and pi (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 11pi/12 value = -(√6+√2)/4 or -0.9659258. . .
Since the cosine function is a periodic function, we can represent cos 11pi/12 as, cos 11pi/12 = cos(11pi/12 + n × 2pi), n ∈ Z.
⇒ cos 11pi/12 = cos 35pi/12 = cos 59pi/12 , and so on.
Note: Since, cosine is an even function, the value of cos(-11pi/12) = cos(11pi/12).

Methods to Find Value of Cos 11pi/12

The cosine function is negative in the 2nd quadrant. The value of cos 11pi/12 is given as -0.96592. . .. We can find the value of cos 11pi/12 by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 11pi/12 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 11pi/12 as:

• ± √(1-sin²(11pi/12))
• ± 1/√(1 + tan²(11pi/12))
• ± cot(11pi/12)/√(1 + cot²(11pi/12))
• ±√(cosec²(11pi/12) - 1)/cosec(11pi/12)
• 1/sec(11pi/12)

Note: Since 11pi/12 lies in the 2nd Quadrant, the final value of cos 11pi/12 will be negative.

We can use trigonometric identities to represent cos 11pi/12 as,

• -cos(pi - 11pi/12) = -cos pi/12
• -cos(pi + 11pi/12) = -cos 23pi/12
• sin(pi/2 + 11pi/12) = sin 17pi/12
• sin(pi/2 - 11pi/12) = sin(-5pi/12)

Cos 11pi/12 Using Unit Circle

To find the value of cos 11π/12 using the unit circle:

• Rotate ‘r’ anticlockwise to form 11pi/12 angle with the positive x-axis.
• The cos of 11pi/12 equals the x-coordinate(-0.9659) of the point of intersection (-0.9659, 0.2588) of unit circle and r.

Hence the value of cos 11pi/12 = x = -0.9659 (approx)

☛ Also Check:

• cos 10pi/3
• cos 9pi/2
• cos 17pi/12
• cos pi/3
• sin pi/6
• cos 7pi/4

FAQs on Cos 11pi/12

What is Cos 11pi/12?

Cos 11pi/12 is the value of cosine trigonometric function for an angle equal to 11π/12 radians. The value of cos 11pi/12 is -(√6+√2)/4 or -0.9659 (approx)

What is the Value of Cos 11pi/12 in Terms of Sin 11pi/12?

Using trigonometric identities, we can write cos 11pi/12 in terms of sin 11pi/12 as, cos(11pi/12) = -√(1 - sin²(11pi/12)). Here, the value of sin 11pi/12 is equal to (√6 - √2)/4.

How to Find the Value of Cos 11pi/12?

The value of cos 11pi/12 can be calculated by constructing an angle of 11π/12 radians with the x-axis, and then finding the coordinates of the corresponding point (-0.9659, 0.2588) on the unit circle. The value of cos 11pi/12 is equal to the x-coordinate (-0.9659). ∴ cos 11pi/12 = -0.9659.

How to Find Cos 11pi/12 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 11pi/12 can be given in terms of other trigonometric functions as:

• ± √(1-sin²(11pi/12))
• ± 1/√(1 + tan²(11pi/12))
• ± cot(11pi/12)/√(1 + cot²(11pi/12))
• ±√(cosec²(11pi/12) - 1)/cosec(11pi/12)
• 1/sec(11pi/12)

☛ Also check: trigonometry table

What is the Exact Value of cos 11pi/12?

The exact value of cos 11pi/12 can be given accurately up to 8 decimal places as -0.96592582 and -(√6+√2)/4 in fraction.