Exact Value Of Cos Pi/4

Cos pi/iv

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

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

What is the Value of Cos pi/4?

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

We know, using radian to caste conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/iv × (180°/pi) = 45° or 45 degrees
∴ cos pi/iv = cos π/iv = cos(45°) = ane/√2 or 0.7071067. . .

Cos pi/4

Explanation:

For cos pi/4, the angle pi/4 lies between 0 and pi/2 (Starting time Quadrant). Since cosine part is positive in the first quadrant, thus cos pi/4 value = 1/√two or 0.7071067. . .
Since the cosine office is a periodic function, nosotros can correspond cos pi/4 as, cos pi/4 = cos(pi/4 + n × 2pi), n ∈ Z.
⇒ cos pi/4 = cos 9pi/four = cos 17pi/4 , and and then on.
Note: Since, cosine is an even function, the value of cos(-pi/4) = cos(pi/four).

Methods to Find Value of Cos pi/4

The cosine function is positive in the 1st quadrant. The value of cos pi/4 is given equally 0.70710. . .. We can find the value of cos pi/four by:

Using Trigonometric Functions
Using Unit Circle

Cos pi/four in Terms of Trigonometric Functions

Using trigonometry formulas, we tin represent the cos pi/4 as:

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

Note: Since pi/four lies in the 1st Quadrant, the final value of cos pi/4 volition be positive.

We can use trigonometric identities to correspond cos pi/4 as,

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

Cos pi/iv Using Unit Circumvolve

value of cos pi/4

To observe the value of cos π/4 using the unit of measurement circumvolve:

Rotate 'r' anticlockwise to form pi/iv angle with the positive 10-axis.
The cos of pi/4 equals the x-coordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit of measurement circumvolve and r.

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

☛ Also Check:

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

FAQs on Cos pi/4

What is Cos pi/4?

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

How to Find 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 as:

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

☛ Also check: trigonometric table

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

Since the cosine role can exist represented using the cosecant function, we can write cos pi/4 as [√(cosec²(pi/4) - 1)/cosec pi/iv]. The value of cosec pi/iv is equal to 1.41421.

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

Nosotros know, using trig identities, we tin can write cos pi/iv as 1/√(one + tan²(pi/4)). Here, the value of tan pi/4 is equal to 1.

How to Find the Value of Cos pi/4?

The value of cos pi/iv can be calculated by constructing an angle of π/4 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/four is equal to the x-coordinate (0.7071). ∴ cos pi/iv = 0.7071.