Sin 315 Degrees
The value of sin 315 degrees is -0.7071067. . .. Sin 315 degrees in radians is written as sin (315° × π/180°), i.e., sin (7π/4) or sin (5.497787. . .). In this article, we will discuss the methods to find the value of sin 315 degrees with examples.
- Sin 315°: -0.7071067. . .
- Sin 315° in fraction: -(1/√2)
- Sin (-315 degrees): 0.7071067. . .
- Sin 315° in radians: sin (7π/4) or sin (5.4977871 . . .)
What is the Value of Sin 315 Degrees?
The value of sin 315 degrees in decimal is -0.707106781. . .. Sin 315 degrees can also be expressed using the equivalent of the given angle (315 degrees) in radians (5.49778 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 315 degrees = 315° × (π/180°) rad = 7π/4 or 5.4977 . . .
∴ sin 315° = sin(5.4977) = -(1/√2) or -0.7071067. . .
Explanation:
For sin 315 degrees, the angle 315° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 315° value = -(1/√2) or -0.7071067. . .
Since the sine function is a periodic function, we can represent sin 315° as, sin 315 degrees = sin(315° + n × 360°), n ∈ Z.
⇒ sin 315° = sin 675° = sin 1035°, and so on.
Note: Since, sine is an odd function, the value of sin(-315°) = -sin(315°).
Methods to Find Value of Sin 315 Degrees
The sine function is negative in the 4th quadrant. The value of sin 315° is given as -0.70710. . .. We can find the value of sin 315 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 315 Degrees Using Unit Circle
To find the value of sin 315 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 315° angle with the positive x-axis.
- The sin of 315 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 315° = y = -0.7071 (approx)
Sin 315° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 315 degrees as:
- ± √(1-cos²(315°))
- ± tan 315°/√(1 + tan²(315°))
- ± 1/√(1 + cot²(315°))
- ± √(sec²(315°) - 1)/sec 315°
- 1/cosec 315°
Note: Since 315° lies in the 4th Quadrant, the final value of sin 315° will be negative.
We can use trigonometric identities to represent sin 315° as,
- sin(180° - 315°) = sin(-135°)
- -sin(180° + 315°) = -sin 495°
- cos(90° - 315°) = cos(-225°)
- -cos(90° + 315°) = -cos 405°
☛ Also Check:
FAQs on Sin 315 Degrees
What is Sin 315 Degrees?
Sin 315 degrees is the value of sine trigonometric function for an angle equal to 315 degrees. The value of sin 315° is -(1/√2) or -0.7071 (approx).
How to Find Sin 315° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 315° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(315°))
- ± tan 315°/√(1 + tan²(315°))
- ± 1/√(1 + cot²(315°))
- ± √(sec²(315°) - 1)/sec 315°
- 1/cosec 315°
☛ Also check: trigonometric table
What is the Value of Sin 315° in Terms of Cosec 315°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 315° as 1/cosec(315°). The value of cosec 315° is equal to -1.41421.
How to Find the Value of Sin 315 Degrees?
The value of sin 315 degrees can be calculated by constructing an angle of 315° 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 315° is equal to the y-coordinate (-0.7071). ∴ sin 315° = -0.7071.
What is the Value of Sin 315 Degrees in Terms of Cot 315°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 315° can be written as -1/√(1 + cot²(315°)). Here, the value of cot 315° is equal to -0.99999.