Sin 960 Degrees
The value of sin 960 degrees is -0.8660254. . .. Sin 960 degrees in radians is written as sin (960° × π/180°), i.e., sin (16π/3) or sin (16.755160. . .). In this article, we will discuss the methods to find the value of sin 960 degrees with examples.
- Sin 960°: -0.8660254. . .
- Sin 960° in fraction: -(√3/2)
- Sin (-960 degrees): 0.8660254. . .
- Sin 960° in radians: sin (16π/3) or sin (16.7551608 . . .)
What is the Value of Sin 960 Degrees?
The value of sin 960 degrees in decimal is -0.866025403. . .. Sin 960 degrees can also be expressed using the equivalent of the given angle (960 degrees) in radians (16.75516 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 960 degrees = 960° × (π/180°) rad = 16π/3 or 16.7551 . . .
∴ sin 960° = sin(16.7551) = -(√3/2) or -0.8660254. . .
Explanation:
For sin 960°, the angle 960° > 360°. Given the periodic property of the sine function, we can represent it as sin(960° mod 360°) = sin(240°). The angle 960°, coterminal to angle 240°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 960 degrees value = -(√3/2) or -0.8660254. . .
Similarly, sin 960° can also be written as, sin 960 degrees = (960° + n × 360°), n ∈ Z.
⇒ sin 960° = sin 1320° = sin 1680°, and so on.
Note: Since, sine is an odd function, the value of sin(-960°) = -sin(960°).
Methods to Find Value of Sin 960 Degrees
The sine function is negative in the 3rd quadrant. The value of sin 960° is given as -0.86602. . .. We can find the value of sin 960 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sin 960 Degrees Using Unit Circle
To find the value of sin 960 degrees using the unit circle, represent 960° in the form (2 × 360°) + 240° [∵ 960°>360°] ∵ sine is a periodic function, sin 960° = sin 240°.
- Rotate ‘r’ anticlockwise to form a 240° or 960° angle with the positive x-axis.
- The sin of 960 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 960° = y = -0.866 (approx)
Sin 960° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 960 degrees as:
- ± √(1-cos²(960°))
- ± tan 960°/√(1 + tan²(960°))
- ± 1/√(1 + cot²(960°))
- ± √(sec²(960°) - 1)/sec 960°
- 1/cosec 960°
Note: Since 960° lies in the 3rd Quadrant, the final value of sin 960° will be negative.
We can use trigonometric identities to represent sin 960° as,
- sin(180° - 960°) = sin(-780°)
- -sin(180° + 960°) = -sin 1140°
- cos(90° - 960°) = cos(-870°)
- -cos(90° + 960°) = -cos 1050°
☛ Also Check:
FAQs on Sin 960 Degrees
What is Sin 960 Degrees?
Sin 960 degrees is the value of sine trigonometric function for an angle equal to 960 degrees. The value of sin 960° is -(√3/2) or -0.866 (approx).
How to Find Sin 960° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 960° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(960°))
- ± tan 960°/√(1 + tan²(960°))
- ± 1/√(1 + cot²(960°))
- ± √(sec²(960°) - 1)/sec 960°
- 1/cosec 960°
☛ Also check: trigonometric table
How to Find the Value of Sin 960 Degrees?
The value of sin 960 degrees can be calculated by constructing an angle of 960° 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 960° is equal to the y-coordinate (-0.866). ∴ sin 960° = -0.866.
What is the Value of Sin 960° in Terms of Sec 960°?
Since the sine function can be represented using the secant function, we can write sin 960° as √(sec²(960°) - 1)/sec 960°. The value of sec 960° is equal to -2.
What is the Value of Sin 960 Degrees in Terms of Cot 960°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 960° can be written as -1/√(1 + cot²(960°)). Here, the value of cot 960° is equal to 0.57735.