Sin 260 Degrees
The value of sin 260 degrees is -0.9848077. . .. Sin 260 degrees in radians is written as sin (260° × π/180°), i.e., sin (13π/9) or sin (4.537856. . .). In this article, we will discuss the methods to find the value of sin 260 degrees with examples.
- Sin 260°: -0.9848077. . .
- Sin (-260 degrees): 0.9848077. . .
- Sin 260° in radians: sin (13π/9) or sin (4.5378560 . . .)
What is the Value of Sin 260 Degrees?
The value of sin 260 degrees in decimal is -0.984807753. . .. Sin 260 degrees can also be expressed using the equivalent of the given angle (260 degrees) in radians (4.53785 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 260 degrees = 260° × (π/180°) rad = 13π/9 or 4.5378 . . .
∴ sin 260° = sin(4.5378) = -0.9848077. . .
Explanation:
For sin 260 degrees, the angle 260° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 260° value = -0.9848077. . .
Since the sine function is a periodic function, we can represent sin 260° as, sin 260 degrees = sin(260° + n × 360°), n ∈ Z.
⇒ sin 260° = sin 620° = sin 980°, and so on.
Note: Since, sine is an odd function, the value of sin(-260°) = -sin(260°).
Methods to Find Value of Sin 260 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 260° is given as -0.98480. . .. We can find the value of sin 260 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 260° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 260 degrees as:
- ± √(1-cos²(260°))
- ± tan 260°/√(1 + tan²(260°))
- ± 1/√(1 + cot²(260°))
- ± √(sec²(260°) - 1)/sec 260°
- 1/cosec 260°
Note: Since 260° lies in the 3rd Quadrant, the final value of sin 260° will be negative.
We can use trigonometric identities to represent sin 260° as,
- sin(180° - 260°) = sin(-80°)
- -sin(180° + 260°) = -sin 440°
- cos(90° - 260°) = cos(-170°)
- -cos(90° + 260°) = -cos 350°
Sin 260 Degrees Using Unit Circle
To find the value of sin 260 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 260° angle with the positive x-axis.
- The sin of 260 degrees equals the y-coordinate(-0.9848) of the point of intersection (-0.1736, -0.9848) of unit circle and r.
Hence the value of sin 260° = y = -0.9848 (approx)
☛ Also Check:
FAQs on Sin 260 Degrees
What is Sin 260 Degrees?
Sin 260 degrees is the value of sine trigonometric function for an angle equal to 260 degrees. The value of sin 260° is -0.9848 (approx).
How to Find Sin 260° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 260° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(260°))
- ± tan 260°/√(1 + tan²(260°))
- ± 1/√(1 + cot²(260°))
- ± √(sec²(260°) - 1)/sec 260°
- 1/cosec 260°
☛ Also check: trigonometric table
What is the Value of Sin 260° in Terms of Cosec 260°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 260° as 1/cosec(260°). The value of cosec 260° is equal to -1.01542.
What is the Value of Sin 260 Degrees in Terms of Cot 260°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 260° can be written as -1/√(1 + cot²(260°)). Here, the value of cot 260° is equal to 0.17632.
How to Find the Value of Sin 260 Degrees?
The value of sin 260 degrees can be calculated by constructing an angle of 260° with the x-axis, and then finding the coordinates of the corresponding point (-0.1736, -0.9848) on the unit circle. The value of sin 260° is equal to the y-coordinate (-0.9848). ∴ sin 260° = -0.9848.