Cos pi/8
The value of cos pi/8 is 0.9238795. . .. Cos pi/8 radians in degrees is written as cos ((π/8) × 180°/π), i.e., cos (22.5°). In this article, we will discuss the methods to find the value of cos pi/8 with examples.
 Cos pi/8 in decimal: 0.9238795. . .
 Cos (pi/8): 0.9238795. . .
 Cos pi/8 in degrees: cos (22.5°)
What is the Value of Cos pi/8?
The value of cos pi/8 in decimal is 0.923879532. . .. Cos pi/8 can also be expressed using the equivalent of the given angle (pi/8) in degrees (22.5°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/8 radians = pi/8 × (180°/pi) = 22.5° or 22.5 degrees
∴ cos pi/8 = cos π/8 = cos(22.5°) = 0.9238795. . .
Explanation:
For cos pi/8, the angle pi/8 lies between 0 and pi/2 (First Quadrant). Since cosine function is positive in the first quadrant, thus cos pi/8 value = 0.9238795. . .
Since the cosine function is a periodic function, we can represent cos pi/8 as, cos pi/8 = cos(pi/8 + n × 2pi), n ∈ Z.
⇒ cos pi/8 = cos 17pi/8 = cos 33pi/8 , and so on.
Note: Since, cosine is an even function, the value of cos(pi/8) = cos(pi/8).
Methods to Find Value of Cos pi/8
The cosine function is positive in the 1st quadrant. The value of cos pi/8 is given as 0.92387. . .. We can find the value of cos pi/8 by:
 Using Unit Circle
 Using Trigonometric Functions
Cos pi/8 Using Unit Circle
To find the value of cos π/8 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/8 angle with the positive xaxis.
 The cos of pi/8 equals the xcoordinate(0.9239) of the point of intersection (0.9239, 0.3827) of unit circle and r.
Hence the value of cos pi/8 = x = 0.9239 (approx)
Cos pi/8 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos pi/8 as:
 ± √(1sin²(pi/8))
 ± 1/√(1 + tan²(pi/8))
 ± cot(pi/8)/√(1 + cot²(pi/8))
 ±√(cosec²(pi/8)  1)/cosec(pi/8)
 1/sec(pi/8)
Note: Since pi/8 lies in the 1st Quadrant, the final value of cos pi/8 will be positive.
We can use trigonometric identities to represent cos pi/8 as,
 cos(pi  pi/8) = cos 7pi/8
 cos(pi + pi/8) = cos 9pi/8
 sin(pi/2 + pi/8) = sin 5pi/8
 sin(pi/2  pi/8) = sin 3pi/8
☛ Also Check:
Examples Using Cos pi/8

Example 1: Find the value of cos pi/8 if sec pi/8 is 1.0823.
Solution:
Since, cos pi/8 = 1/sec(pi/8)
⇒ cos pi/8 = 1/1.0823 = 0.9239 
Example 2: Using the value of cos pi/8, solve: (1sin²(pi/8)).
Solution:
We know, (1sin²(pi/8)) = (cos²(pi/8)) = 0.8536
⇒ (1sin²(pi/8)) = 0.8536 
Example 3: Find the value of (cos² pi/16  sin² pi/16). [Hint: Use cos pi/8 = 0.9239]
Solution:
Using the cos 2a formula,
(cos² pi/16  sin² pi/16) = cos(2 × pi/16) = cos pi/8
∵ cos pi/8 = 0.9239
⇒ (cos² pi/16  sin² pi/16) = 0.9239
FAQs on Cos pi/8
What is Cos pi/8?
Cos pi/8 is the value of cosine trigonometric function for an angle equal to π/8 radians. The value of cos pi/8 is 0.9239 (approx)
How to Find Cos pi/8 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos pi/8 can be given in terms of other trigonometric functions as:
 ± √(1sin²(pi/8))
 ± 1/√(1 + tan²(pi/8))
 ± cot(pi/8)/√(1 + cot²(pi/8))
 ±√(cosec²(pi/8)  1)/cosec(pi/8)
 1/sec(pi/8)
☛ Also check: trigonometry table
What is the Value of Cos pi/8 in Terms of Cot pi/8?
We can represent the cosine function in terms of the cotangent function using trig identities, cos pi/8 can be written as cot(pi/8)/√(1 + cot²(pi/8)). Here, the value of cot pi/8 is equal to 2.41421.
What is the Value of Cos pi/8 in Terms of Cosec pi/8?
Since the cosine function can be represented using the cosecant function, we can write cos pi/8 as [√(cosec²(pi/8)  1)/cosec pi/8]. The value of cosec pi/8 is equal to 2.61312.
How to Find the Value of Cos pi/8?
The value of cos pi/8 can be calculated by constructing an angle of π/8 radians with the xaxis, and then finding the coordinates of the corresponding point (0.9239, 0.3827) on the unit circle. The value of cos pi/8 is equal to the xcoordinate (0.9239). ∴ cos pi/8 = 0.9239.
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