Sin 135 Degrees
The value of sin 135 degrees is 0.7071067. . .. Sin 135 degrees in radians is written as sin (135° × π/180°), i.e., sin (3π/4) or sin (2.356194. . .). In this article, we will discuss the methods to find the value of sin 135 degrees with examples.
- Sin 135°: 0.7071067. . .
- Sin 135° in fraction: 1/√2
- Sin (-135 degrees): -0.7071067. . .
- Sin 135° in radians: sin (3π/4) or sin (2.3561944 . . .)
What is the Value of Sin 135 Degrees?
The value of sin 135 degrees in decimal is 0.707106781. . .. Sin 135 degrees can also be expressed using the equivalent of the given angle (135 degrees) in radians (2.35619 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 135 degrees = 135° × (π/180°) rad = 3π/4 or 2.3561 . . .
∴ sin 135° = sin(2.3561) = 1/√2 or 0.7071067. . .
Explanation:
For sin 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 135° value = 1/√2 or 0.7071067. . .
Since the sine function is a periodic function, we can represent sin 135° as, sin 135 degrees = sin(135° + n × 360°), n ∈ Z.
⇒ sin 135° = sin 495° = sin 855°, and so on.
Note: Since, sine is an odd function, the value of sin(-135°) = -sin(135°).
Methods to Find Value of Sin 135 Degrees
The sine function is positive in the 2nd quadrant. The value of sin 135° is given as 0.70710. . .. We can find the value of sin 135 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 135° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 135 degrees as:
- ± √(1-cos²(135°))
- ± tan 135°/√(1 + tan²(135°))
- ± 1/√(1 + cot²(135°))
- ± √(sec²(135°) - 1)/sec 135°
- 1/cosec 135°
Note: Since 135° lies in the 2nd Quadrant, the final value of sin 135° will be positive.
We can use trigonometric identities to represent sin 135° as,
- sin(180° - 135°) = sin 45°
- -sin(180° + 135°) = -sin 315°
- cos(90° - 135°) = cos(-45°)
- -cos(90° + 135°) = -cos 225°
Sin 135 Degrees Using Unit Circle
To find the value of sin 135 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 135° angle with the positive x-axis.
- The sin of 135 degrees equals the y-coordinate(0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r.
Hence the value of sin 135° = y = 0.7071 (approx)
☛ Also Check:
FAQs on Sin 135 Degrees
What is Sin 135 Degrees?
Sin 135 degrees is the value of sine trigonometric function for an angle equal to 135 degrees. The value of sin 135° is 1/√2 or 0.7071 (approx).
What is the Exact Value of sin 135 Degrees?
The exact value of sin 135 degrees can be given accurately up to 8 decimal places as 0.70710678 and 1/√2 in fraction.
How to Find the Value of Sin 135 Degrees?
The value of sin 135 degrees can be calculated by constructing an angle of 135° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of sin 135° is equal to the y-coordinate (0.7071). ∴ sin 135° = 0.7071.
How to Find Sin 135° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 135° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(135°))
- ± tan 135°/√(1 + tan²(135°))
- ± 1/√(1 + cot²(135°))
- ± √(sec²(135°) - 1)/sec 135°
- 1/cosec 135°
☛ Also check: trigonometry table
What is the Value of Sin 135 Degrees in Terms of Cos 135°?
Using trigonometric identities, we can write sin 135° in terms of cos 135° as, sin(135°) = √(1-cos²(135°)). Here, the value of cos 135° is equal to −(1/√2) .