Sin 600 Degrees
The value of sin 600 degrees is -0.8660254. . .. Sin 600 degrees in radians is written as sin (600° × π/180°), i.e., sin (10π/3) or sin (10.471975. . .). In this article, we will discuss the methods to find the value of sin 600 degrees with examples.
- Sin 600°: -0.8660254. . .
- Sin 600° in fraction: -(√3/2)
- Sin (-600 degrees): 0.8660254. . .
- Sin 600° in radians: sin (10π/3) or sin (10.4719755 . . .)
What is the Value of Sin 600 Degrees?
The value of sin 600 degrees in decimal is -0.866025403. . .. Sin 600 degrees can also be expressed using the equivalent of the given angle (600 degrees) in radians (10.47197 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 600 degrees = 600° × (π/180°) rad = 10π/3 or 10.4719 . . .
∴ sin 600° = sin(10.4719) = -(√3/2) or -0.8660254. . .
Explanation:
For sin 600°, the angle 600° > 360°. Given the periodic property of the sine function, we can represent it as sin(600° mod 360°) = sin(240°). The angle 600°, coterminal to angle 240°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 600 degrees value = -(√3/2) or -0.8660254. . .
Similarly, sin 600° can also be written as, sin 600 degrees = (600° + n × 360°), n ∈ Z.
⇒ sin 600° = sin 960° = sin 1320°, and so on.
Note: Since, sine is an odd function, the value of sin(-600°) = -sin(600°).
Methods to Find Value of Sin 600 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 600° is given as -0.86602. . .. We can find the value of sin 600 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 600 Degrees Using Unit Circle
To find the value of sin 600 degrees using the unit circle, represent 600° in the form (1 × 360°) + 240° [∵ 600°>360°] ∵ sine is a periodic function, sin 600° = sin 240°.
- Rotate ‘r’ anticlockwise to form a 240° or 600° angle with the positive x-axis.
- The sin of 600 degrees equals the y-coordinate(-0.866) of the point of intersection (-0.5, -0.866) of unit circle and r.
Hence the value of sin 600° = y = -0.866 (approx)
Sin 600° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 600 degrees as:
- ± √(1-cos²(600°))
- ± tan 600°/√(1 + tan²(600°))
- ± 1/√(1 + cot²(600°))
- ± √(sec²(600°) - 1)/sec 600°
- 1/cosec 600°
Note: Since 600° lies in the 3rd Quadrant, the final value of sin 600° will be negative.
We can use trigonometric identities to represent sin 600° as,
- sin(180° - 600°) = sin(-420°)
- -sin(180° + 600°) = -sin 780°
- cos(90° - 600°) = cos(-510°)
- -cos(90° + 600°) = -cos 690°
☛ Also Check:
FAQs on Sin 600 Degrees
What is Sin 600 Degrees?
Sin 600 degrees is the value of sine trigonometric function for an angle equal to 600 degrees. The value of sin 600° is -(√3/2) or -0.866 (approx).
How to Find Sin 600° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 600° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(600°))
- ± tan 600°/√(1 + tan²(600°))
- ± 1/√(1 + cot²(600°))
- ± √(sec²(600°) - 1)/sec 600°
- 1/cosec 600°
☛ Also check: trigonometric table
How to Find the Value of Sin 600 Degrees?
The value of sin 600 degrees can be calculated by constructing an angle of 600° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of sin 600° is equal to the y-coordinate (-0.866). ∴ sin 600° = -0.866.
What is the Value of Sin 600 Degrees in Terms of Tan 600°?
We know, using trig identities, we can write sin 600° as -tan 600°/√(1 + tan²(600°)). Here, the value of tan 600° is equal to 1.732050.
What is the Value of Sin 600° in Terms of Sec 600°?
Since the sine function can be represented using the secant function, we can write sin 600° as √(sec²(600°) - 1)/sec 600°. The value of sec 600° is equal to -2.