Exact Value Of Sin Pi/4

Sin 3pi/4

The value of sin 3pi/4 is 0.7071067. . .. Sin 3pi/4 radians in degrees is written as sin ((3π/4) × 180°/π), i.eastward., sin (135°). In this article, we volition talk over the methods to detect the value of sin 3pi/iv with examples.

Sin 3pi/4: 1/√2
Sin 3pi/iv in decimal: 0.7071067. . .
Sin (-3pi/4): -0.7071067. . . or -(ane/√two)
Sin 3pi/iv in degrees: sin (135°)

What is the Value of Sin 3pi/4?

The value of sin 3pi/4 in decimal is 0.707106781. . .. Sin 3pi/4 can also exist expressed using the equivalent of the given bending (3pi/4) in degrees (135°).

Nosotros know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 3pi/4 radians = 3pi/4 × (180°/pi) = 135° or 135 degrees
∴ sin 3pi/4 = sin 3π/4 = sin(135°) = 1/√2 or 0.7071067. . .

Sin 3pi/4

Explanation:

For sin 3pi/4, the angle 3pi/4 lies between pi/2 and pi (Second Quadrant). Since sine office is positive in the second quadrant, thus sin 3pi/four value = one/√2 or 0.7071067. . .
Since the sine role is a periodic role, nosotros tin can represent sin 3pi/four as, sin 3pi/four = sin(3pi/4 + due north × 2pi), n ∈ Z.
⇒ sin 3pi/4 = sin 11pi/4 = sin 19pi/iv , and and so on.
Annotation: Since, sine is an odd function, the value of sin(-3pi/4) = -sin(3pi/4).

Methods to Find Value of Sin 3pi/4

The sine role is positive in the 2d quadrant. The value of sin 3pi/four is given as 0.70710. . .. We tin discover the value of sin 3pi/four past:

Using Trigonometric Functions
Using Unit Circumvolve

Sin 3pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 3pi/four as:

± √(1-cos²(3pi/4))
± tan(3pi/four)/√(1 + tan²(3pi/four))
± i/√(one + cot²(3pi/4))
± √(sec²(3pi/4) - 1)/sec(3pi/iv)
ane/cosec(3pi/4)

Notation: Since 3pi/4 lies in the 2nd Quadrant, the last value of sin 3pi/iv will be positive.

We tin utilise trigonometric identities to stand for sin 3pi/iv as,

sin(pi - 3pi/iv) = sin pi/4
-sin(pi + 3pi/4) = -sin 7pi/4
cos(pi/2 - 3pi/iv) = cos(-pi/iv)
-cos(pi/two + 3pi/iv) = -cos 5pi/4

Sin 3pi/4 Using Unit Circle

value of sin 3pi/4

To find the value of sin 3π/iv using the unit of measurement circumvolve:

Rotate 'r' anticlockwise to form 3pi/4 angle with the positive x-axis.
The sin of 3pi/four equals the y-coordinate(0.7071) of the point of intersection (-0.7071, 0.7071) of unit of measurement circumvolve and r.

Hence the value of sin 3pi/4 = y = 0.7071 (approx)

☛ Likewise Check:

cot 5pi/three
sec pi
tan 2pi
sin 5pi/four
cos pi
cos 2pi/3

FAQs on Sin 3pi/4

What is Sin 3pi/4?

Sin 3pi/iv is the value of sine trigonometric function for an bending equal to 3pi/4 radians. The value of sin 3pi/4 is 1/√2 or 0.7071 (approx).

How to Observe the Value of Sin 3pi/4?

The value of sin 3pi/4 can be calculated by amalgam an angle of 3π/4 radians with the ten-centrality, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit of measurement circumvolve. The value of sin 3pi/4 is equal to the y-coordinate (0.7071). ∴ sin 3pi/4 = 0.7071.

What is the Value of Sin 3pi/iv in Terms of Cosec 3pi/4?

Since the cosecant function is the reciprocal of the sine part, we tin write sin 3pi/four as 1/cosec(3pi/4). The value of cosec 3pi/four is equal to 1.41421.

How to Find Sin 3pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 3π/4 can be given in terms of other trigonometric functions as:

± √(1-cos²(3pi/4))
± tan(3pi/4)/√(1 + tan²(3pi/4))
± i/√(1 + cot²(3pi/4))
± √(sec²(3pi/4) - 1)/sec(3pi/four)
1/cosec(3pi/4)

☛ Besides check: trigonometric tabular array

What is the Value of Sin 3pi/4 in Terms of Cos 3pi/iv?

Using trigonometric identities, we can write sin 3pi/four in terms of cos 3pi/iv as, sin(3pi/iv) = √(i-cos²(3pi/4)). Here, the value of cos 3pi/4 is equal to −(one/√2) .