Sin 1000 Degrees
The value of sin 1000 degrees is -0.9848077. . .. Sin 1000 degrees in radians is written as sin (1000° × π/180°), i.e., sin (50π/9) or sin (17.453292. . .). In this article, we will discuss the methods to find the value of sin 1000 degrees with examples.
- Sin 1000°: -0.9848077. . .
- Sin (-1000 degrees): 0.9848077. . .
- Sin 1000° in radians: sin (50π/9) or sin (17.4532925 . . .)
What is the Value of Sin 1000 Degrees?
The value of sin 1000 degrees in decimal is -0.984807753. . .. Sin 1000 degrees can also be expressed using the equivalent of the given angle (1000 degrees) in radians (17.45329 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1000 degrees = 1000° × (π/180°) rad = 50π/9 or 17.4532 . . .
∴ sin 1000° = sin(17.4532) = -0.9848077. . .
Explanation:
For sin 1000°, the angle 1000° > 360°. Given the periodic property of the sine function, we can represent it as sin(1000° mod 360°) = sin(280°). The angle 1000°, coterminal to angle 280°, is located in the Fourth Quadrant(Quadrant IV).
Since sine function is negative in the 4th quadrant, thus sin 1000 degrees value = -0.9848077. . .
Similarly, sin 1000° can also be written as, sin 1000 degrees = (1000° + n × 360°), n ∈ Z.
⇒ sin 1000° = sin 1360° = sin 1720°, and so on.
Note: Since, sine is an odd function, the value of sin(-1000°) = -sin(1000°).
Methods to Find Value of Sin 1000 Degrees
The sine function is negative in the 4th quadrant. The value of sin 1000° is given as -0.98480. . .. We can find the value of sin 1000 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 1000° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 1000 degrees as:
- ± √(1-cos²(1000°))
- ± tan 1000°/√(1 + tan²(1000°))
- ± 1/√(1 + cot²(1000°))
- ± √(sec²(1000°) - 1)/sec 1000°
- 1/cosec 1000°
Note: Since 1000° lies in the 4th Quadrant, the final value of sin 1000° will be negative.
We can use trigonometric identities to represent sin 1000° as,
- sin(180° - 1000°) = sin(-820°)
- -sin(180° + 1000°) = -sin 1180°
- cos(90° - 1000°) = cos(-910°)
- -cos(90° + 1000°) = -cos 1090°
Sin 1000 Degrees Using Unit Circle
To find the value of sin 1000 degrees using the unit circle, represent 1000° in the form (2 × 360°) + 280° [∵ 1000°>360°] ∵ sine is a periodic function, sin 1000° = sin 280°.
- Rotate ‘r’ anticlockwise to form a 280° or 1000° angle with the positive x-axis.
- The sin of 1000 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 1000° = y = -0.9848 (approx)
☛ Also Check:
FAQs on Sin 1000 Degrees
What is Sin 1000 Degrees?
Sin 1000 degrees is the value of sine trigonometric function for an angle equal to 1000 degrees. The value of sin 1000° is -0.9848 (approx).
What is the Value of Sin 1000 Degrees in Terms of Tan 1000°?
We know, using trig identities, we can write sin 1000° as tan 1000°/√(1 + tan²(1000°)). Here, the value of tan 1000° is equal to -5.671281.
What is the Exact Value of sin 1000 Degrees?
The exact value of sin 1000 degrees can be given accurately up to 8 decimal places as -0.98480775.
How to Find the Value of Sin 1000 Degrees?
The value of sin 1000 degrees can be calculated by constructing an angle of 1000° 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 1000° is equal to the y-coordinate (-0.9848). ∴ sin 1000° = -0.9848.
How to Find Sin 1000° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 1000° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(1000°))
- ± tan 1000°/√(1 + tan²(1000°))
- ± 1/√(1 + cot²(1000°))
- ± √(sec²(1000°) - 1)/sec 1000°
- 1/cosec 1000°
☛ Also check: trigonometry table