Sin 910 Degrees
The value of sin 910 degrees is -0.1736481. . .. Sin 910 degrees in radians is written as sin (910° × π/180°), i.e., sin (91π/18) or sin (15.882496. . .). In this article, we will discuss the methods to find the value of sin 910 degrees with examples.
- Sin 910°: -0.1736481. . .
- Sin (-910 degrees): 0.1736481. . .
- Sin 910° in radians: sin (91π/18) or sin (15.8824961 . . .)
What is the Value of Sin 910 Degrees?
The value of sin 910 degrees in decimal is -0.173648177. . .. Sin 910 degrees can also be expressed using the equivalent of the given angle (910 degrees) in radians (15.88249 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 910 degrees = 910° × (π/180°) rad = 91π/18 or 15.8824 . . .
∴ sin 910° = sin(15.8824) = -0.1736481. . .
Explanation:
For sin 910°, the angle 910° > 360°. Given the periodic property of the sine function, we can represent it as sin(910° mod 360°) = sin(190°). The angle 910°, coterminal to angle 190°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 910 degrees value = -0.1736481. . .
Similarly, sin 910° can also be written as, sin 910 degrees = (910° + n × 360°), n ∈ Z.
⇒ sin 910° = sin 1270° = sin 1630°, and so on.
Note: Since, sine is an odd function, the value of sin(-910°) = -sin(910°).
Methods to Find Value of Sin 910 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 910° is given as -0.17364. . .. We can find the value of sin 910 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 910 Degrees Using Unit Circle
To find the value of sin 910 degrees using the unit circle, represent 910° in the form (2 × 360°) + 190° [∵ 910°>360°] ∵ sine is a periodic function, sin 910° = sin 190°.
- Rotate ‘r’ anticlockwise to form a 190° or 910° angle with the positive x-axis.
- The sin of 910 degrees equals the y-coordinate(-0.1736) of the point of intersection (-0.9848, -0.1736) of unit circle and r.
Hence the value of sin 910° = y = -0.1736 (approx)
Sin 910° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 910 degrees as:
- ± √(1-cos²(910°))
- ± tan 910°/√(1 + tan²(910°))
- ± 1/√(1 + cot²(910°))
- ± √(sec²(910°) - 1)/sec 910°
- 1/cosec 910°
Note: Since 910° lies in the 3rd Quadrant, the final value of sin 910° will be negative.
We can use trigonometric identities to represent sin 910° as,
- sin(180° - 910°) = sin(-730°)
- -sin(180° + 910°) = -sin 1090°
- cos(90° - 910°) = cos(-820°)
- -cos(90° + 910°) = -cos 1000°
☛ Also Check:
FAQs on Sin 910 Degrees
What is Sin 910 Degrees?
Sin 910 degrees is the value of sine trigonometric function for an angle equal to 910 degrees. The value of sin 910° is -0.1736 (approx).
What is the Value of Sin 910 Degrees in Terms of Cos 910°?
Using trigonometric identities, we can write sin 910° in terms of cos 910° as, sin(910°) = -√(1-cos²(910°)). Here, the value of cos 910° is equal to -0.9848077.
What is the Exact Value of sin 910 Degrees?
The exact value of sin 910 degrees can be given accurately up to 8 decimal places as -0.17364817.
How to Find Sin 910° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 910° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(910°))
- ± tan 910°/√(1 + tan²(910°))
- ± 1/√(1 + cot²(910°))
- ± √(sec²(910°) - 1)/sec 910°
- 1/cosec 910°
☛ Also check: trigonometry table
How to Find the Value of Sin 910 Degrees?
The value of sin 910 degrees can be calculated by constructing an angle of 910° with the x-axis, and then finding the coordinates of the corresponding point (-0.9848, -0.1736) on the unit circle. The value of sin 910° is equal to the y-coordinate (-0.1736). ∴ sin 910° = -0.1736.