Cos 11pi/4
The value of cos 11pi/4 is 0.7071067. . .. Cos 11pi/4 radians in degrees is written as cos ((11π/4) × 180°/π), i.e., cos (495°). In this article, we will discuss the methods to find the value of cos 11pi/4 with examples.
 Cos 11pi/4: −(1/√2)
 Cos 11pi/4 in decimal: 0.7071067. . .
 Cos (11pi/4): 0.7071067. . . or (1/√2)
 Cos 11pi/4 in degrees: cos (495°)
What is the Value of Cos 11pi/4?
The value of cos 11pi/4 in decimal is 0.707106781. . .. Cos 11pi/4 can also be expressed using the equivalent of the given angle (11pi/4) in degrees (495°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/4 radians = 11pi/4 × (180°/pi) = 495° or 495 degrees
∴ cos 11pi/4 = cos 11π/4 = cos(495°) = −(1/√2) or 0.7071067. . .
Explanation:
For cos 11pi/4, the angle 11pi/4 > 2pi. Given the periodic property of the cosine function, we can represent it as cos(11pi/4 mod 2pi) = cos(3pi/4). The angle 11pi/4, coterminal to angle 3pi/4, is located in the Second Quadrant(Quadrant II).
Since cos function is negative in the 2nd quadrant, thus cos 11pi/4 value = −(1/√2) or 0.7071067. . .
Similarly, cos 11pi/4 can also be written as, cos 11pi/4 = (11pi/4 + n × 2pi), n ∈ Z.
⇒ cos 11pi/4 = cos 19pi/4 = cos 27pi/4, and so on.
Note: Since, cosine is an even function, the value of cos(11pi/4) = cos(11pi/4).
Methods to Find Value of Cos 11pi/4
The cosine function is negative in the 2nd quadrant. The value of cos 11pi/4 is given as 0.70710. . .. We can find the value of cos 11pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Cos 11pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 11pi/4 as:
 ± √(1sin²(11pi/4))
 ± 1/√(1 + tan²(11pi/4))
 ± cot(11pi/4)/√(1 + cot²(11pi/4))
 ±√(cosec²(11pi/4)  1)/cosec(11pi/4)
 1/sec(11pi/4)
Note: Since 11pi/4 lies in the 2nd Quadrant, the final value of cos 11pi/4 will be negative.
We can use trigonometric identities to represent cos 11pi/4 as,
 cos(pi  11pi/4) = cos(7pi/4)
 cos(pi + 11pi/4) = cos 15pi/4
 sin(pi/2 + 11pi/4) = sin 13pi/4
 sin(pi/2  11pi/4) = sin(9pi/4)
Cos 11pi/4 Using Unit Circle
To find the value of cos 11π/4 using the unit circle, represent 11pi/4 in the form (1 × 2pi) + 3pi/4 [∵ 11pi/4>2pi] ∵ cosine is a periodic function, cos 11pi/4 = cos 3pi/4.
 Rotate ‘r’ anticlockwise to form 3pi/4 or 11pi/4 angle with the positive xaxis.
 The cos of 11pi/4 equals the xcoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of cos 11pi/4 = x = 0.7071 (approx)
☛ Also Check:
Examples Using Cos 11pi/4

Example 1: Find the value of (cos² 11pi/8  sin² 11pi/8). [Hint: Use cos 11pi/4 = 0.7071]
Solution:
Using the cos 2a formula,
(cos² 11pi/8  sin² 11pi/8) = cos(2 × 11pi/8) = cos 11pi/4
∵ cos 11pi/4 = 0.7071
⇒ (cos² 11pi/8  sin² 11pi/8) = 0.7071 
Example 2: Using the value of cos 11pi/4, solve: (1sin²(11pi/4)).
Solution:
We know, (1sin²(11pi/4)) = (cos²(11pi/4)) = 0.5
⇒ (1sin²(11pi/4)) = 0.5 
Example 3: Find the value of 2 cos(11pi/4)/3 sin(9pi/4).
Solution:
Using trigonometric identities, we know, cos(11pi/4) = sin(pi/2  11pi/4) = sin(9pi/4).
⇒ cos(11pi/4) = sin(9pi/4)
⇒ Value of 2 cos(11pi/4)/3 sin(9pi/4) = 2/3
FAQs on Cos 11pi/4
What is Cos 11pi/4?
Cos 11pi/4 is the value of cosine trigonometric function for an angle equal to 11π/4 radians. The value of cos 11pi/4 is −(1/√2) or 0.7071 (approx)
How to Find the Value of Cos 11pi/4?
The value of cos 11pi/4 can be calculated by constructing an angle of 11π/4 radians with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cos 11pi/4 is equal to the xcoordinate (0.7071). ∴ cos 11pi/4 = 0.7071.
How to Find Cos 11pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 11pi/4 can be given in terms of other trigonometric functions as:
 ± √(1sin²(11pi/4))
 ± 1/√(1 + tan²(11pi/4))
 ± cot(11pi/4)/√(1 + cot²(11pi/4))
 ±√(cosec²(11pi/4)  1)/cosec(11pi/4)
 1/sec(11pi/4)
☛ Also check: trigonometry table
What is the Value of Cos 11pi/4 in Terms of Cot 11pi/4?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 11pi/4 can be written as cot(11pi/4)/√(1 + cot²(11pi/4)). Here, the value of cot 11pi/4 is equal to 1.
What is the Value of Cos 11pi/4 in Terms of Sec 11pi/4?
Since the secant function is the reciprocal of the cosine function, we can write cos 11pi/4 as 1/sec(11pi/4). The value of sec 11pi/4 is equal to 1.414213.
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