Cos 0 8

Cos pi/8

The value of
cos pi/viii 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/viii 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 exist expressed using the equivalent of the given angle (pi/viii) in degrees (22.5°).

We know, using radian to caste conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/8 radians = pi/8 × (180°/pi) = 22.5° or 22.v 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 (Showtime Quadrant). Since cosine function is positive in the first quadrant, thus cos pi/8 value = 0.9238795. . .
Since the cosine function is a periodic part, we tin correspond cos pi/viii as, cos pi/8 = cos(pi/8 + n × 2pi), n ∈ Z.
⇒ cos pi/8 = cos 17pi/8 = cos 33pi/8 , and and so on.
Notation:
Since, cosine is an even part, the value of cos(-pi/viii) = 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/eight is given equally 0.92387. . .. We can find the value of cos pi/viii past:

• Using Unit Circle
• Using Trigonometric Functions

Cos pi/viii Using Unit Circumvolve

To find the value of cos π/8 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/viii angle with the positive x-centrality.
• The cos of pi/eight equals the x-coordinate(0.9239) of the indicate of intersection (0.9239, 0.3827) of unit circumvolve and r.

Hence the value of cos pi/8 = ten = 0.9239 (approx)

Cos pi/8 in Terms of Trigonometric Functions

Using trigonometry formulas, we can correspond the cos pi/8 as:

• ± √(1-sin²(pi/8))
• ± 1/√(one + tan²(pi/eight))
• ± cot(pi/8)/√(ane + cot²(pi/8))
• ±√(cosec²(pi/8) – i)/cosec(pi/8)
• 1/sec(pi/eight)

Note:
Since pi/eight lies in the 1st Quadrant, the last value of cos pi/8 volition be positive.

We tin can use trigonometric identities to correspond 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/eight) = sin 3pi/eight

☛ Also Check:

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

FAQs on Cos pi/8

What is Cos pi/eight?

Cos pi/8 is the value of cosine trigonometric function for an angle equal to π/8 radians.


The value of cos pi/viii is 0.9239 (approx)

How to Notice Cos pi/eight in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos pi/8 tin exist given in terms of other trigonometric functions as:

• ± √(1-sin²(pi/8))
• ± 1/√(1 + tan²(pi/eight))
• ± cot(pi/8)/√(1 + cot²(pi/8))
• ±√(cosec²(pi/8) – 1)/cosec(pi/8)
• 1/sec(pi/8)

☛ Also bank check: trigonometry table

What is the Value of Cos pi/8 in Terms of Cot pi/8?

We tin represent the cosine function in terms of the cotangent part using trig identities, cos pi/8 can be written equally cot(pi/8)/√(1 + cot²(pi/eight)). Here, the value of cot pi/eight is equal to 2.41421.

What is the Value of Cos pi/viii in Terms of Cosec pi/8?

Since the cosine function can be represented using the cosecant part, we can write cos pi/viii every bit [√(cosec²(pi/8) – 1)/cosec pi/8]. The value of cosec pi/8 is equal to 2.61312.

How to Notice the Value of Cos pi/8?

The value of cos pi/8 tin be calculated by constructing an bending of π/8 radians with the x-centrality, and and then finding the coordinates of the corresponding point (0.9239, 0.3827) on the unit circle. The value of cos pi/eight is equal to the x-coordinate (0.9239). ∴ cos pi/8 = 0.9239.