Sin 120 Degrees

The value of sin 120 degrees is 0.8660254. . .. Sin 120 degrees in radians is written as sin (120° × π/180°), i.e., sin (2π/3) or sin (2.094395. . .). In this article, we will discuss the methods to find the value of sin 120 degrees with examples.

• Sin 120°: 0.8660254. . .
• Sin 120° in fraction: √3/2
• Sin (-120 degrees): -0.8660254. . .
• Sin 120° in radians: sin (2π/3) or sin (2.0943951 . . .)

What is the Value of Sin 120 Degrees?

The value of sin 120 degrees in decimal is 0.866025403. . .. Sin 120 degrees can also be expressed using the equivalent of the given angle (120 degrees) in radians (2.09439 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 120 degrees = 120° × (π/180°) rad = 2π/3 or 2.0943 . . .
∴ sin 120° = sin(2.0943) = √3/2 or 0.8660254. . .

Explanation:

For sin 120 degrees, the angle 120° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 120° value = √3/2 or 0.8660254. . .
Since the sine function is a periodic function, we can represent sin 120° as, sin 120 degrees = sin(120° + n × 360°), n ∈ Z.
⇒ sin 120° = sin 480° = sin 840°, and so on.
Note: Since, sine is an odd function, the value of sin(-120°) = -sin(120°).

Methods to Find Value of Sin 120 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 120° is given as 0.86602. . .. We can find the value of sin 120 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 120 Degrees Using Unit Circle

To find the value of sin 120 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 120° angle with the positive x-axis.
• The sin of 120 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 120° = y = 0.866 (approx)

Sin 120° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 120 degrees as:

• ± √(1-cos²(120°))
• ± tan 120°/√(1 + tan²(120°))
• ± 1/√(1 + cot²(120°))
• ± √(sec²(120°) - 1)/sec 120°
• 1/cosec 120°

Note: Since 120° lies in the 2nd Quadrant, the final value of sin 120° will be positive.

We can use trigonometric identities to represent sin 120° as,

• sin(180° - 120°) = sin 60°
• -sin(180° + 120°) = -sin 300°
• cos(90° - 120°) = cos(-30°)
• -cos(90° + 120°) = -cos 210°

☛ Also Check:

• sin 50 degrees
• sin 0 degrees
• sin 75 degrees
• sin 47 degrees
• sin 206 degrees
• sin 23 degrees

FAQs on Sin 120 Degrees

What is Sin 120 Degrees?

Sin 120 degrees is the value of sine trigonometric function for an angle equal to 120 degrees. The value of sin 120° is √3/2 or 0.866 (approx).

What is the Value of Sin 120 Degrees in Terms of Tan 120°?

We know, using trig identities, we can write sin 120° as -tan 120°/√(1 + tan²(120°)). Here, the value of tan 120° is equal to -1.732050.

How to Find the Value of Sin 120 Degrees?

The value of sin 120 degrees can be calculated by constructing an angle of 120° 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 120° is equal to the y-coordinate (0.866). ∴ sin 120° = 0.866.

What is the Value of Sin 120° in Terms of Cosec 120°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 120° as 1/cosec(120°). The value of cosec 120° is equal to 1.15470.

How to Find Sin 120° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 120° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(120°))
• ± tan 120°/√(1 + tan²(120°))
• ± 1/√(1 + cot²(120°))
• ± √(sec²(120°) - 1)/sec 120°
• 1/cosec 120°

☛ Also check: trigonometric table