Sin 26 Degrees
The value of sin 26 degrees is 0.4383711. . .. Sin 26 degrees in radians is written as sin (26° × π/180°), i.e., sin (13π/90) or sin (0.453785. . .). In this article, we will discuss the methods to find the value of sin 26 degrees with examples.
- Sin 26°: 0.4383711. . .
- Sin (-26 degrees): -0.4383711. . .
- Sin 26° in radians: sin (13π/90) or sin (0.4537856 . . .)
What is the Value of Sin 26 Degrees?
The value of sin 26 degrees in decimal is 0.438371146. . .. Sin 26 degrees can also be expressed using the equivalent of the given angle (26 degrees) in radians (0.45378 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 26 degrees = 26° × (π/180°) rad = 13π/90 or 0.4537 . . .
∴ sin 26° = sin(0.4537) = 0.4383711. . .
Explanation:
For sin 26 degrees, the angle 26° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 26° value = 0.4383711. . .
Since the sine function is a periodic function, we can represent sin 26° as, sin 26 degrees = sin(26° + n × 360°), n ∈ Z.
⇒ sin 26° = sin 386° = sin 746°, and so on.
Note: Since, sine is an odd function, the value of sin(-26°) = -sin(26°).
Methods to Find Value of Sin 26 Degrees
The sine function is positive in the 1st quadrant. The value of sin 26° is given as 0.43837. . .. We can find the value of sin 26 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 26° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 26 degrees as:
- ± √(1-cos²(26°))
- ± tan 26°/√(1 + tan²(26°))
- ± 1/√(1 + cot²(26°))
- ± √(sec²(26°) - 1)/sec 26°
- 1/cosec 26°
Note: Since 26° lies in the 1st Quadrant, the final value of sin 26° will be positive.
We can use trigonometric identities to represent sin 26° as,
- sin(180° - 26°) = sin 154°
- -sin(180° + 26°) = -sin 206°
- cos(90° - 26°) = cos 64°
- -cos(90° + 26°) = -cos 116°
Sin 26 Degrees Using Unit Circle
To find the value of sin 26 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 26° angle with the positive x-axis.
- The sin of 26 degrees equals the y-coordinate(0.4384) of the point of intersection (0.8988, 0.4384) of unit circle and r.
Hence the value of sin 26° = y = 0.4384 (approx)
☛ Also Check:
FAQs on Sin 26 Degrees
What is Sin 26 Degrees?
Sin 26 degrees is the value of sine trigonometric function for an angle equal to 26 degrees. The value of sin 26° is 0.4384 (approx).
What is the Value of Sin 26 Degrees in Terms of Cos 26°?
Using trigonometric identities, we can write sin 26° in terms of cos 26° as, sin(26°) = √(1-cos²(26°)). Here, the value of cos 26° is equal to 0.8987940.
What is the Value of Sin 26° in Terms of Cosec 26°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 26° as 1/cosec(26°). The value of cosec 26° is equal to 2.28117.
How to Find Sin 26° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 26° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(26°))
- ± tan 26°/√(1 + tan²(26°))
- ± 1/√(1 + cot²(26°))
- ± √(sec²(26°) - 1)/sec 26°
- 1/cosec 26°
☛ Also check: trigonometry table
How to Find the Value of Sin 26 Degrees?
The value of sin 26 degrees can be calculated by constructing an angle of 26° with the x-axis, and then finding the coordinates of the corresponding point (0.8988, 0.4384) on the unit circle. The value of sin 26° is equal to the y-coordinate (0.4384). ∴ sin 26° = 0.4384.