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:

• ± √(1-sin²(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 x-axis.
• The cos of 11pi/4 equals the x-coordinate(-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:

• cot 3pi/4
• cos 5pi/12
• sin pi
• cot pi/2
• csc pi/6
• cos 2pi/8

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 x-axis, 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 x-coordinate (-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:

• ± √(1-sin²(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.