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 x-axis.
• The cos of pi/8 equals the x-coordinate(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:

• ± √(1-sin²(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:

• cot pi/2
• cos 2pi/3
• sin pi/8
• cos 3pi/2
• cot pi/3
• sin pi/4

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:

• ± √(1-sin²(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 x-axis, 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 x-coordinate (0.9239). ∴ cos pi/8 = 0.9239.