Sin 60 Degrees
The value of sin 60 degrees is 0.8660254. . .. Sin 60 degrees in radians is written as sin (60° × π/180°), i.e., sin (π/3) or sin (1.047197. . .). In this article, we will discuss the methods to find the value of sin 60 degrees with examples.
 Sin 60°: 0.8660254. . .
 Sin 60° in fraction: √3/2
 Sin (60 degrees): 0.8660254. . .
 Sin 60° in radians: sin (π/3) or sin (1.0471975 . . .)
What is the Value of Sin 60 Degrees?
The value of sin 60 degrees in decimal is 0.866025403. . .. Sin 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ sin 60° = sin(1.0471) = √3/2 or 0.8660254. . .
Explanation:
For sin 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 60° value = √3/2 or 0.8660254. . .
Since the sine function is a periodic function, we can represent sin 60° as, sin 60 degrees = sin(60° + n × 360°), n ∈ Z.
⇒ sin 60° = sin 420° = sin 780°, and so on.
Note: Since, sine is an odd function, the value of sin(60°) = sin(60°).
Methods to Find Value of Sin 60 Degrees
The sine function is positive in the 1st quadrant. The value of sin 60° is given as 0.86602. . .. We can find the value of sin 60 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 60° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 60 degrees as:
 ± √(1cos²(60°))
 ± tan 60°/√(1 + tan²(60°))
 ± 1/√(1 + cot²(60°))
 ± √(sec²(60°)  1)/sec 60°
 1/cosec 60°
Note: Since 60° lies in the 1st Quadrant, the final value of sin 60° will be positive.
We can use trigonometric identities to represent sin 60° as,
 sin(180°  60°) = sin 120°
 sin(180° + 60°) = sin 240°
 cos(90°  60°) = cos 30°
 cos(90° + 60°) = cos 150°
Sin 60 Degrees Using Unit Circle
To find the value of sin 60 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 60° angle with the positive xaxis.
 The sin of 60 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 60° = y = 0.866 (approx)
☛ Also Check:
Examples Using Sin 60 Degrees

Example 1: Find the value of 2 × (sin 30° cos 30°). [Hint: Use sin 60° = 0.866]
Solution:
Using the sin 2a formula,
2 sin 30° cos 30° = sin(2 × 30°) = sin 60°
∵ sin 60° = 0.866
⇒ 2 × (sin 30° cos 30°) = 0.866 
Example 2: Simplify: 2 (sin 60°/sin 420°)
Solution:
We know sin 60° = sin 420°
⇒ 2 sin 60°/sin 420° = 2(sin 60°/sin 60°)
= 2(1) = 2 
Example 3: Find the value of sin 60° if cosec 60° is 1.1547.
Solution:
Since, sin 60° = 1/csc 60°
⇒ sin 60° = 1/1.1547 = 0.866
FAQs on Sin 60 Degrees
What is Sin 60 Degrees?
Sin 60 degrees is the value of sine trigonometric function for an angle equal to 60 degrees. The value of sin 60° is √3/2 or 0.866 (approx).
What is the Value of Sin 60 Degrees in Terms of Tan 60°?
We know, using trig identities, we can write sin 60° as tan 60°/√(1 + tan²(60°)). Here, the value of tan 60° is equal to 1.732050.
How to Find Sin 60° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 60° can be given in terms of other trigonometric functions as:
 ± √(1cos²(60°))
 ± tan 60°/√(1 + tan²(60°))
 ± 1/√(1 + cot²(60°))
 ± √(sec²(60°)  1)/sec 60°
 1/cosec 60°
☛ Also check: trigonometry table
How to Find the Value of Sin 60 Degrees?
The value of sin 60 degrees can be calculated by constructing an angle of 60° with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of sin 60° is equal to the ycoordinate (0.866). ∴ sin 60° = 0.866.
What is the Exact Value of sin 60 Degrees?
The exact value of sin 60 degrees can be given accurately up to 8 decimal places as 0.86602540 and √3/2 in fraction.
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