Sin 25 Degrees
The value of sin 25 degrees is 0.4226182. . .. Sin 25 degrees in radians is written as sin (25° × π/180°), i.e., sin (5π/36) or sin (0.436332. . .). In this article, we will discuss the methods to find the value of sin 25 degrees with examples.
- Sin 25°: 0.4226182. . .
- Sin (-25 degrees): -0.4226182. . .
- Sin 25° in radians: sin (5π/36) or sin (0.4363323 . . .)
What is the Value of Sin 25 Degrees?
The value of sin 25 degrees in decimal is 0.422618261. . .. Sin 25 degrees can also be expressed using the equivalent of the given angle (25 degrees) in radians (0.43633 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 25 degrees = 25° × (π/180°) rad = 5π/36 or 0.4363 . . .
∴ sin 25° = sin(0.4363) = 0.4226182. . .
Explanation:
For sin 25 degrees, the angle 25° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 25° value = 0.4226182. . .
Since the sine function is a periodic function, we can represent sin 25° as, sin 25 degrees = sin(25° + n × 360°), n ∈ Z.
⇒ sin 25° = sin 385° = sin 745°, and so on.
Note: Since, sine is an odd function, the value of sin(-25°) = -sin(25°).
Methods to Find Value of Sin 25 Degrees
The sine function is positive in the 1st quadrant. The value of sin 25° is given as 0.42261. . .. We can find the value of sin 25 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 25° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 25 degrees as:
- ± √(1-cos²(25°))
- ± tan 25°/√(1 + tan²(25°))
- ± 1/√(1 + cot²(25°))
- ± √(sec²(25°) - 1)/sec 25°
- 1/cosec 25°
Note: Since 25° lies in the 1st Quadrant, the final value of sin 25° will be positive.
We can use trigonometric identities to represent sin 25° as,
- sin(180° - 25°) = sin 155°
- -sin(180° + 25°) = -sin 205°
- cos(90° - 25°) = cos 65°
- -cos(90° + 25°) = -cos 115°
Sin 25 Degrees Using Unit Circle
To find the value of sin 25 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 25° angle with the positive x-axis.
- The sin of 25 degrees equals the y-coordinate(0.4226) of the point of intersection (0.9063, 0.4226) of unit circle and r.
Hence the value of sin 25° = y = 0.4226 (approx)
☛ Also Check:
FAQs on Sin 25 Degrees
What is Sin 25 Degrees?
Sin 25 degrees is the value of sine trigonometric function for an angle equal to 25 degrees. The value of sin 25° is 0.4226 (approx).
How to Find the Value of Sin 25 Degrees?
The value of sin 25 degrees can be calculated by constructing an angle of 25° with the x-axis, and then finding the coordinates of the corresponding point (0.9063, 0.4226) on the unit circle. The value of sin 25° is equal to the y-coordinate (0.4226). ∴ sin 25° = 0.4226.
How to Find Sin 25° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 25° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(25°))
- ± tan 25°/√(1 + tan²(25°))
- ± 1/√(1 + cot²(25°))
- ± √(sec²(25°) - 1)/sec 25°
- 1/cosec 25°
☛ Also check: trigonometry table
What is the Exact Value of sin 25 Degrees?
The exact value of sin 25 degrees can be given accurately up to 8 decimal places as 0.42261826.
What is the Value of Sin 25 Degrees in Terms of Cot 25°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 25° can be written as 1/√(1 + cot²(25°)). Here, the value of cot 25° is equal to 2.14450.