Sin 225 Degrees
The value of sin 225 degrees is -0.7071067. . .. Sin 225 degrees in radians is written as sin (225° × π/180°), i.e., sin (5π/4) or sin (3.926990. . .). In this article, we will discuss the methods to find the value of sin 225 degrees with examples.
- Sin 225°: -0.7071067. . .
- Sin 225° in fraction: -(1/√2)
- Sin (-225 degrees): 0.7071067. . .
- Sin 225° in radians: sin (5π/4) or sin (3.9269908 . . .)
What is the Value of Sin 225 Degrees?
The value of sin 225 degrees in decimal is -0.707106781. . .. Sin 225 degrees can also be expressed using the equivalent of the given angle (225 degrees) in radians (3.92699 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 225 degrees = 225° × (π/180°) rad = 5π/4 or 3.9269 . . .
∴ sin 225° = sin(3.9269) = -(1/√2) or -0.7071067. . .
Explanation:
For sin 225 degrees, the angle 225° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 225° value = -(1/√2) or -0.7071067. . .
Since the sine function is a periodic function, we can represent sin 225° as, sin 225 degrees = sin(225° + n × 360°), n ∈ Z.
⇒ sin 225° = sin 585° = sin 945°, and so on.
Note: Since, sine is an odd function, the value of sin(-225°) = -sin(225°).
Methods to Find Value of Sin 225 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 225° is given as -0.70710. . .. We can find the value of sin 225 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 225° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 225 degrees as:
- ± √(1-cos²(225°))
- ± tan 225°/√(1 + tan²(225°))
- ± 1/√(1 + cot²(225°))
- ± √(sec²(225°) - 1)/sec 225°
- 1/cosec 225°
Note: Since 225° lies in the 3rd Quadrant, the final value of sin 225° will be negative.
We can use trigonometric identities to represent sin 225° as,
- sin(180° - 225°) = sin(-45°)
- -sin(180° + 225°) = -sin 405°
- cos(90° - 225°) = cos(-135°)
- -cos(90° + 225°) = -cos 315°
Sin 225 Degrees Using Unit Circle
To find the value of sin 225 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 225° angle with the positive x-axis.
- The sin of 225 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 225° = y = -0.7071 (approx)
☛ Also Check:
FAQs on Sin 225 Degrees
What is Sin 225 Degrees?
Sin 225 degrees is the value of sine trigonometric function for an angle equal to 225 degrees. The value of sin 225° is -(1/√2) or -0.7071 (approx).
What is the Value of Sin 225° in Terms of Cosec 225°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 225° as 1/cosec(225°). The value of cosec 225° is equal to -1.41421.
How to Find Sin 225° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 225° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(225°))
- ± tan 225°/√(1 + tan²(225°))
- ± 1/√(1 + cot²(225°))
- ± √(sec²(225°) - 1)/sec 225°
- 1/cosec 225°
☛ Also check: trigonometry table
What is the Value of Sin 225 Degrees in Terms of Cos 225°?
Using trigonometric identities, we can write sin 225° in terms of cos 225° as, sin(225°) = -√(1-cos²(225°)). Here, the value of cos 225° is equal to -(1/√2).
How to Find the Value of Sin 225 Degrees?
The value of sin 225 degrees can be calculated by constructing an angle of 225° 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 225° is equal to the y-coordinate (-0.7071). ∴ sin 225° = -0.7071.