Sin 1125 Degrees
The value of sin 1125 degrees is 0.7071067. . .. Sin 1125 degrees in radians is written as sin (1125° × π/180°), i.e., sin (25π/4) or sin (19.634954. . .). In this article, we will discuss the methods to find the value of sin 1125 degrees with examples.
- Sin 1125°: 0.7071067. . .
- Sin 1125° in fraction: 1/√2
- Sin (-1125 degrees): -0.7071067. . .
- Sin 1125° in radians: sin (25π/4) or sin (19.6349540 . . .)
What is the Value of Sin 1125 Degrees?
The value of sin 1125 degrees in decimal is 0.707106781. . .. Sin 1125 degrees can also be expressed using the equivalent of the given angle (1125 degrees) in radians (19.63495 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1125 degrees = 1125° × (π/180°) rad = 25π/4 or 19.6349 . . .
∴ sin 1125° = sin(19.6349) = 1/√2 or 0.7071067. . .
Explanation:
For sin 1125°, the angle 1125° > 360°. Given the periodic property of the sine function, we can represent it as sin(1125° mod 360°) = sin(45°). The angle 1125°, coterminal to angle 45°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 1125 degrees value = 1/√2 or 0.7071067. . .
Similarly, sin 1125° can also be written as, sin 1125 degrees = (1125° + n × 360°), n ∈ Z.
⇒ sin 1125° = sin 1485° = sin 1845°, and so on.
Note: Since, sine is an odd function, the value of sin(-1125°) = -sin(1125°).
Methods to Find Value of Sin 1125 Degrees
The sine function is positive in the 1st quadrant. The value of sin 1125° is given as 0.70710. . .. We can find the value of sin 1125 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 1125° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 1125 degrees as:
- ± √(1-cos²(1125°))
- ± tan 1125°/√(1 + tan²(1125°))
- ± 1/√(1 + cot²(1125°))
- ± √(sec²(1125°) - 1)/sec 1125°
- 1/cosec 1125°
Note: Since 1125° lies in the 1st Quadrant, the final value of sin 1125° will be positive.
We can use trigonometric identities to represent sin 1125° as,
- sin(180° - 1125°) = sin(-945°)
- -sin(180° + 1125°) = -sin 1305°
- cos(90° - 1125°) = cos(-1035°)
- -cos(90° + 1125°) = -cos 1215°
Sin 1125 Degrees Using Unit Circle
To find the value of sin 1125 degrees using the unit circle, represent 1125° in the form (3 × 360°) + 45° [∵ 1125°>360°] ∵ sine is a periodic function, sin 1125° = sin 45°.
- Rotate ‘r’ anticlockwise to form a 45° or 1125° angle with the positive x-axis.
- The sin of 1125 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 1125° = y = 0.7071 (approx)
☛ Also Check:
FAQs on Sin 1125 Degrees
What is Sin 1125 Degrees?
Sin 1125 degrees is the value of sine trigonometric function for an angle equal to 1125 degrees. The value of sin 1125° is 1/√2 or 0.7071 (approx).
How to Find the Value of Sin 1125 Degrees?
The value of sin 1125 degrees can be calculated by constructing an angle of 1125° 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 1125° is equal to the y-coordinate (0.7071). ∴ sin 1125° = 0.7071.
How to Find Sin 1125° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 1125° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(1125°))
- ± tan 1125°/√(1 + tan²(1125°))
- ± 1/√(1 + cot²(1125°))
- ± √(sec²(1125°) - 1)/sec 1125°
- 1/cosec 1125°
☛ Also check: trigonometry table
What is the Exact Value of sin 1125 Degrees?
The exact value of sin 1125 degrees can be given accurately up to 8 decimal places as 0.70710678 and 1/√2 in fraction.
What is the Value of Sin 1125 Degrees in Terms of Cos 1125°?
Using trigonometric identities, we can write sin 1125° in terms of cos 1125° as, sin(1125°) = √(1-cos²(1125°)). Here, the value of cos 1125° is equal to 0.7071067.