Sin 240 Degrees

The value of sin 240 degrees is -0.8660254. . .. Sin 240 degrees in radians is written as sin (240° × π/180°), i.e., sin (4π/3) or sin (4.188790. . .). In this article, we will discuss the methods to find the value of sin 240 degrees with examples.

• Sin 240°: -0.8660254. . .
• Sin 240° in fraction: -(√3/2)
• Sin (-240 degrees): 0.8660254. . .
• Sin 240° in radians: sin (4π/3) or sin (4.1887902 . . .)

What is the Value of Sin 240 Degrees?

The value of sin 240 degrees in decimal is -0.866025403. . .. Sin 240 degrees can also be expressed using the equivalent of the given angle (240 degrees) in radians (4.18879 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 240 degrees = 240° × (π/180°) rad = 4π/3 or 4.1887 . . .
∴ sin 240° = sin(4.1887) = -(√3/2) or -0.8660254. . .

Explanation:

For sin 240 degrees, the angle 240° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 240° value = -(√3/2) or -0.8660254. . .
Since the sine function is a periodic function, we can represent sin 240° as, sin 240 degrees = sin(240° + n × 360°), n ∈ Z.
⇒ sin 240° = sin 600° = sin 960°, and so on.
Note: Since, sine is an odd function, the value of sin(-240°) = -sin(240°).

Methods to Find Value of Sin 240 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 240° is given as -0.86602. . .. We can find the value of sin 240 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 240° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 240 degrees as:

• ± √(1-cos²(240°))
• ± tan 240°/√(1 + tan²(240°))
• ± 1/√(1 + cot²(240°))
• ± √(sec²(240°) - 1)/sec 240°
• 1/cosec 240°

Note: Since 240° lies in the 3rd Quadrant, the final value of sin 240° will be negative.

We can use trigonometric identities to represent sin 240° as,

• sin(180° - 240°) = sin(-60°)
• -sin(180° + 240°) = -sin 420°
• cos(90° - 240°) = cos(-150°)
• -cos(90° + 240°) = -cos 330°

Sin 240 Degrees Using Unit Circle

To find the value of sin 240 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 240° angle with the positive x-axis.
• The sin of 240 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 240° = y = -0.866 (approx)

☛ Also Check:

• sin 0 degrees
• sin 15 degrees
• sin 150 degrees
• sin 600 degrees
• sin 510 degrees
• sin 33 degrees

FAQs on Sin 240 Degrees

What is Sin 240 Degrees?

Sin 240 degrees is the value of sine trigonometric function for an angle equal to 240 degrees. The value of sin 240° is -(√3/2) or -0.866 (approx).

What is the Value of Sin 240° in Terms of Sec 240°?

Since the sine function can be represented using the secant function, we can write sin 240° as √(sec²(240°) - 1)/sec 240°. The value of sec 240° is equal to -2.

What is the Value of Sin 240 Degrees in Terms of Tan 240°?

We know, using trig identities, we can write sin 240° as -tan 240°/√(1 + tan²(240°)). Here, the value of tan 240° is equal to 1.732050.

How to Find Sin 240° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 240° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(240°))
• ± tan 240°/√(1 + tan²(240°))
• ± 1/√(1 + cot²(240°))
• ± √(sec²(240°) - 1)/sec 240°
• 1/cosec 240°

☛ Also check: trigonometry table

How to Find the Value of Sin 240 Degrees?

The value of sin 240 degrees can be calculated by constructing an angle of 240° 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 240° is equal to the y-coordinate (-0.866). ∴ sin 240° = -0.866.