Cos Pi 4 Exact Value

Cos pi/4

The value of cos pi/4 is 0.7071067. . .. Cos pi/4 radians in degrees is written as cos ((π/4) × 180°/π), i.e., cos (45°). In this article, we volition discuss the methods to find the value of cos pi/iv with examples.

Cos pi/iv: 1/√2
Cos pi/iv in decimal: 0.7071067. . .
Cos (-pi/4): 0.7071067. . . or one/√2
Cos pi/4 in degrees: cos (45°)

What is the Value of Cos pi/four?

The value of cos pi/iv in decimal is 0.707106781. . .. Cos pi/iv can also be expressed using the equivalent of the given angle (pi/4) in degrees (45°).

Nosotros know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/4 × (180°/pi) = 45° or 45 degrees
∴ cos pi/four = cos π/four = cos(45°) = one/√2 or 0.7071067. . .

Cos pi/4

Explanation:

For cos pi/4, the angle pi/4 lies between 0 and pi/2 (Kickoff Quadrant). Since cosine function is positive in the commencement quadrant, thus cos pi/4 value = 1/√2 or 0.7071067. . .
Since the cosine role is a periodic function, we tin stand for cos pi/4 as, cos pi/four = cos(pi/4 + n × 2pi), n ∈ Z.
⇒ cos pi/4 = cos 9pi/four = cos 17pi/4 , and so on.
Note: Since, cosine is an even part, the value of cos(-pi/iv) = cos(pi/iv).

Methods to Detect Value of Cos pi/4

The cosine function is positive in the 1st quadrant. The value of cos pi/4 is given as 0.70710. . .. We tin detect the value of cos pi/4 past:

Using Trigonometric Functions
Using Unit Circumvolve

Cos pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, nosotros tin stand for the cos pi/four as:

± √(1-sin²(pi/4))
± i/√(1 + tan²(pi/4))
± cot(pi/4)/√(1 + cot²(pi/4))
±√(cosec²(pi/4) - 1)/cosec(pi/four)
ane/sec(pi/4)

Annotation: Since pi/iv lies in the 1st Quadrant, the last value of cos pi/four will be positive.

Nosotros tin utilize trigonometric identities to represent cos pi/4 as,

-cos(pi - pi/4) = -cos 3pi/4
-cos(pi + pi/4) = -cos 5pi/four
sin(pi/2 + pi/4) = sin 3pi/4
sin(pi/2 - pi/four) = sin pi/4

Cos pi/4 Using Unit of measurement Circumvolve

value of cos pi/4

To find the value of cos π/iv using the unit of measurement circumvolve:

Rotate 'r' anticlockwise to form pi/4 bending with the positive x-centrality.
The cos of pi/4 equals the 10-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.

Hence the value of cos pi/4 = 10 = 0.7071 (approx)

☛ Too Cheque:

sin 5pi/6
cos 7pi/4
cos 3pi/4
cot 2pi/iii
tan pi
sin pi/vi

FAQs on Cos pi/4

What is Cos pi/four?

Cos pi/4 is the value of cosine trigonometric part for an angle equal to π/4 radians. The value of cos pi/4 is 1/√2 or 0.7071 (approx)

How to Observe Cos pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos pi/4 can be given in terms of other trigonometric functions every bit:

± √(1-sin²(pi/four))
± one/√(one + tan²(pi/4))
± cot(pi/4)/√(i + cot²(pi/iv))
±√(cosec²(pi/4) - 1)/cosec(pi/four)
ane/sec(pi/iv)

☛ Besides bank check: trigonometric table

What is the Value of Cos pi/4 in Terms of Cosec pi/4?

Since the cosine function tin be represented using the cosecant part, we can write cos pi/4 every bit [√(cosec²(pi/4) - one)/cosec pi/iv]. The value of cosec pi/4 is equal to 1.41421.

What is the Value of Cos pi/4 in Terms of Tan pi/4?

Nosotros know, using trig identities, nosotros can write cos pi/iv as ane/√(one + tan²(pi/four)). Here, the value of tan pi/4 is equal to i.

How to Find the Value of Cos pi/iv?

The value of cos pi/4 tin be calculated past amalgam an bending of π/four radians with the x-axis, and and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cos pi/4 is equal to the ten-coordinate (0.7071). ∴ cos pi/4 = 0.7071.