Sin 140 Degrees

The value of sin 140 degrees is 0.6427876. . .. Sin 140 degrees in radians is written as sin (140° × π/180°), i.e., sin (7π/9) or sin (2.443460. . .). In this article, we will discuss the methods to find the value of sin 140 degrees with examples.

• Sin 140°: 0.6427876. . .
• Sin (-140 degrees): -0.6427876. . .
• Sin 140° in radians: sin (7π/9) or sin (2.4434609 . . .)

What is the Value of Sin 140 Degrees?

The value of sin 140 degrees in decimal is 0.642787609. . .. Sin 140 degrees can also be expressed using the equivalent of the given angle (140 degrees) in radians (2.44346 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 140 degrees = 140° × (π/180°) rad = 7π/9 or 2.4434 . . .
∴ sin 140° = sin(2.4434) = 0.6427876. . .

Explanation:

For sin 140 degrees, the angle 140° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 140° value = 0.6427876. . .
Since the sine function is a periodic function, we can represent sin 140° as, sin 140 degrees = sin(140° + n × 360°), n ∈ Z.
⇒ sin 140° = sin 500° = sin 860°, and so on.
Note: Since, sine is an odd function, the value of sin(-140°) = -sin(140°).

Methods to Find Value of Sin 140 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 140° is given as 0.64278. . .. We can find the value of sin 140 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 140° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 140 degrees as:

• ± √(1-cos²(140°))
• ± tan 140°/√(1 + tan²(140°))
• ± 1/√(1 + cot²(140°))
• ± √(sec²(140°) - 1)/sec 140°
• 1/cosec 140°

Note: Since 140° lies in the 2nd Quadrant, the final value of sin 140° will be positive.

We can use trigonometric identities to represent sin 140° as,

• sin(180° - 140°) = sin 40°
• -sin(180° + 140°) = -sin 320°
• cos(90° - 140°) = cos(-50°)
• -cos(90° + 140°) = -cos 230°

Sin 140 Degrees Using Unit Circle

To find the value of sin 140 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 140° angle with the positive x-axis.
• The sin of 140 degrees equals the y-coordinate(0.6428) of the point of intersection (-0.766, 0.6428) of unit circle and r.

Hence the value of sin 140° = y = 0.6428 (approx)

☛ Also Check:

• sin 10 degrees
• sin 20 degrees
• sin 37 degrees
• sin 230 degrees
• sin 158 degrees
• sin 1500 degrees

FAQs on Sin 140 Degrees

What is Sin 140 Degrees?

Sin 140 degrees is the value of sine trigonometric function for an angle equal to 140 degrees. The value of sin 140° is 0.6428 (approx).

What is the Value of Sin 140° in Terms of Cosec 140°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 140° as 1/cosec(140°). The value of cosec 140° is equal to 1.55572.

How to Find the Value of Sin 140 Degrees?

The value of sin 140 degrees can be calculated by constructing an angle of 140° with the x-axis, and then finding the coordinates of the corresponding point (-0.766, 0.6428) on the unit circle. The value of sin 140° is equal to the y-coordinate (0.6428). ∴ sin 140° = 0.6428.

What is the Value of Sin 140 Degrees in Terms of Cot 140°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 140° can be written as 1/√(1 + cot²(140°)). Here, the value of cot 140° is equal to -1.19175.

How to Find Sin 140° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 140° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(140°))
• ± tan 140°/√(1 + tan²(140°))
• ± 1/√(1 + cot²(140°))
• ± √(sec²(140°) - 1)/sec 140°
• 1/cosec 140°

☛ Also check: trigonometry table