Cos 11pi/6
The value of cos 11pi/6 is 0.8660254. . .. Cos 11pi/6 radians in degrees is written as cos ((11π/6) × 180°/π), i.e., cos (330°). In this article, we will discuss the methods to find the value of cos 11pi/6 with examples.
- Cos 11pi/6: √3/2
- Cos 11pi/6 in decimal: 0.8660254. . .
- Cos (-11pi/6): 0.8660254. . . or √3/2
- Cos 11pi/6 in degrees: cos (330°)
What is the Value of Cos 11pi/6?
The value of cos 11pi/6 in decimal is 0.866025403. . .. Cos 11pi/6 can also be expressed using the equivalent of the given angle (11pi/6) in degrees (330°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/6 radians = 11pi/6 × (180°/pi) = 330° or 330 degrees
∴ cos 11pi/6 = cos 11π/6 = cos(330°) = √3/2 or 0.8660254. . .
Explanation:
For cos 11pi/6, the angle 11pi/6 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 11pi/6 value = √3/2 or 0.8660254. . .
Since the cosine function is a periodic function, we can represent cos 11pi/6 as, cos 11pi/6 = cos(11pi/6 + n × 2pi), n ∈ Z.
⇒ cos 11pi/6 = cos 23pi/6 = cos 35pi/6 , and so on.
Note: Since, cosine is an even function, the value of cos(-11pi/6) = cos(11pi/6).
Methods to Find Value of Cos 11pi/6
The cosine function is positive in the 4th quadrant. The value of cos 11pi/6 is given as 0.86602. . .. We can find the value of cos 11pi/6 by:
- Using Unit Circle
- Using Trigonometric Functions
Cos 11pi/6 Using Unit Circle
To find the value of cos 11π/6 using the unit circle:
- Rotate ‘r’ anticlockwise to form 11pi/6 angle with the positive x-axis.
- The cos of 11pi/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 11pi/6 = x = 0.866 (approx)
Cos 11pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 11pi/6 as:
- ± √(1-sin²(11pi/6))
- ± 1/√(1 + tan²(11pi/6))
- ± cot(11pi/6)/√(1 + cot²(11pi/6))
- ±√(cosec²(11pi/6) - 1)/cosec(11pi/6)
- 1/sec(11pi/6)
Note: Since 11pi/6 lies in the 4th Quadrant, the final value of cos 11pi/6 will be positive.
We can use trigonometric identities to represent cos 11pi/6 as,
- -cos(pi - 11pi/6) = -cos(-5pi/6)
- -cos(pi + 11pi/6) = -cos 17pi/6
- sin(pi/2 + 11pi/6) = sin 7pi/3
- sin(pi/2 - 11pi/6) = sin(-4pi/3)
☛ Also Check:
FAQs on Cos 11pi/6
What is Cos 11pi/6?
Cos 11pi/6 is the value of cosine trigonometric function for an angle equal to 11π/6 radians. The value of cos 11pi/6 is √3/2 or 0.866 (approx)
What is the Exact Value of cos 11pi/6?
The exact value of cos 11pi/6 can be given accurately up to 8 decimal places as 0.86602540 and √3/2 in fraction.
How to Find Cos 11pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 11pi/6 can be given in terms of other trigonometric functions as:
- ± √(1-sin²(11pi/6))
- ± 1/√(1 + tan²(11pi/6))
- ± cot(11pi/6)/√(1 + cot²(11pi/6))
- ±√(cosec²(11pi/6) - 1)/cosec(11pi/6)
- 1/sec(11pi/6)
☛ Also check: trigonometry table
How to Find the Value of Cos 11pi/6?
The value of cos 11pi/6 can be calculated by constructing an angle of 11π/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 11pi/6 is equal to the x-coordinate (0.866). ∴ cos 11pi/6 = 0.866.
What is the Value of Cos 11pi/6 in Terms of Tan 11pi/6?
We know, using trig identities, we can write cos 11pi/6 as 1/√(1 + tan²(11pi/6)). Here, the value of tan 11pi/6 is equal to -0.577350.