Sin 660 Degrees
The value of sin 660 degrees is 0.8660254. . .. Sin 660 degrees in radians is written as sin (660° × π/180°), i.e., sin (11π/3) or sin (11.519173. . .). In this article, we will discuss the methods to find the value of sin 660 degrees with examples.
 Sin 660°: 0.8660254. . .
 Sin 660° in fraction: (√3/2)
 Sin (660 degrees): 0.8660254. . .
 Sin 660° in radians: sin (11π/3) or sin (11.5191730 . . .)
What is the Value of Sin 660 Degrees?
The value of sin 660 degrees in decimal is 0.866025403. . .. Sin 660 degrees can also be expressed using the equivalent of the given angle (660 degrees) in radians (11.51917 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 660 degrees = 660° × (π/180°) rad = 11π/3 or 11.5191 . . .
∴ sin 660° = sin(11.5191) = (√3/2) or 0.8660254. . .
Explanation:
For sin 660°, the angle 660° > 360°. Given the periodic property of the sine function, we can represent it as sin(660° mod 360°) = sin(300°). The angle 660°, coterminal to angle 300°, is located in the Fourth Quadrant(Quadrant IV).
Since sine function is negative in the 4th quadrant, thus sin 660 degrees value = (√3/2) or 0.8660254. . .
Similarly, sin 660° can also be written as, sin 660 degrees = (660° + n × 360°), n ∈ Z.
⇒ sin 660° = sin 1020° = sin 1380°, and so on.
Note: Since, sine is an odd function, the value of sin(660°) = sin(660°).
Methods to Find Value of Sin 660 Degrees
The sine function is negative in the 4th quadrant. The value of sin 660° is given as 0.86602. . .. We can find the value of sin 660 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 660° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 660 degrees as:
 ± √(1cos²(660°))
 ± tan 660°/√(1 + tan²(660°))
 ± 1/√(1 + cot²(660°))
 ± √(sec²(660°)  1)/sec 660°
 1/cosec 660°
Note: Since 660° lies in the 4th Quadrant, the final value of sin 660° will be negative.
We can use trigonometric identities to represent sin 660° as,
 sin(180°  660°) = sin(480°)
 sin(180° + 660°) = sin 840°
 cos(90°  660°) = cos(570°)
 cos(90° + 660°) = cos 750°
Sin 660 Degrees Using Unit Circle
To find the value of sin 660 degrees using the unit circle, represent 660° in the form (1 × 360°) + 300° [∵ 660°>360°] ∵ sine is a periodic function, sin 660° = sin 300°.
 Rotate ‘r’ anticlockwise to form a 300° or 660° angle with the positive xaxis.
 The sin of 660 degrees equals the ycoordinate(0.866) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of sin 660° = y = 0.866 (approx)
☛ Also Check:
Examples Using Sin 660 Degrees

Example 1: Using the value of sin 660°, solve: (1cos²(660°)).
Solution:
We know, (1cos²(660°)) = (sin²(660°)) = 0.75
⇒ (1cos²(660°)) = 0.75 
Example 2: Simplify: 2 (sin 660°/sin 1380°)
Solution:
We know sin 660° = sin 1380°
⇒ 2 sin 660°/sin 1380° = 2(sin 660°/sin 660°)
= 2(1) = 2 
Example 3: Find the value of 5 sin(660°)/7 cos(570°).
Solution:
Using trigonometric identities, we know, sin(660°) = cos(90°  660°) = cos(570°).
⇒ sin(660°) = cos(570°)
⇒ Value of 5 sin(660°)/7 cos(570°) = 5/7
FAQs on Sin 660 Degrees
What is Sin 660 Degrees?
Sin 660 degrees is the value of sine trigonometric function for an angle equal to 660 degrees. The value of sin 660° is (√3/2) or 0.866 (approx).
What is the Value of Sin 660 Degrees in Terms of Cot 660°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 660° can be written as 1/√(1 + cot²(660°)). Here, the value of cot 660° is equal to 0.57735.
What is the Exact Value of sin 660 Degrees?
The exact value of sin 660 degrees can be given accurately up to 8 decimal places as 0.86602540 and (√3/2) in fraction.
How to Find the Value of Sin 660 Degrees?
The value of sin 660 degrees can be calculated by constructing an angle of 660° with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of sin 660° is equal to the ycoordinate (0.866). ∴ sin 660° = 0.866.
How to Find Sin 660° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 660° can be given in terms of other trigonometric functions as:
 ± √(1cos²(660°))
 ± tan 660°/√(1 + tan²(660°))
 ± 1/√(1 + cot²(660°))
 ± √(sec²(660°)  1)/sec 660°
 1/cosec 660°
☛ Also check: trigonometry table
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