Cos 140 Degrees

The value of cos 140 degrees is -0.7660444. . .. Cos 140 degrees in radians is written as cos (140° × π/180°), i.e., cos (7π/9) or cos (2.443460. . .). In this article, we will discuss the methods to find the value of cos 140 degrees with examples.

• Cos 140°: -0.7660444. . .
• Cos (-140 degrees): -0.7660444. . .
• Cos 140° in radians: cos (7π/9) or cos (2.4434609 . . .)

What is the Value of Cos 140 Degrees?

The value of cos 140 degrees in decimal is -0.766044443. . .. Cos 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 . . .
∴ cos 140° = cos(2.4434) = -0.7660444. . .

Explanation:

For cos 140 degrees, the angle 140° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 140° value = -0.7660444. . .
Since the cosine function is a periodic function, we can represent cos 140° as, cos 140 degrees = cos(140° + n × 360°), n ∈ Z.
⇒ cos 140° = cos 500° = cos 860°, and so on.
Note: Since, cosine is an even function, the value of cos(-140°) = cos(140°).

Methods to Find Value of Cos 140 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 140° is given as -0.76604. . .. We can find the value of cos 140 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 140 Degrees Using Unit Circle

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

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

Hence the value of cos 140° = x = -0.766 (approx)

Cos 140° in Terms of Trigonometric Functions

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

• ± √(1-sin²(140°))
• ± 1/√(1 + tan²(140°))
• ± cot 140°/√(1 + cot²(140°))
• ±√(cosec²(140°) - 1)/cosec 140°
• 1/sec 140°

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

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

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

☛ Also Check:

• cos 18 degrees
• cos 30 degrees
• cos 45 degrees
• cos 200 degrees
• cos 720 degrees
• cos 155 degrees

FAQs on Cos 140 Degrees

What is Cos 140 Degrees?

Cos 140 degrees is the value of cosine trigonometric function for an angle equal to 140 degrees. The value of cos 140° is -0.766 (approx)

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

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

• ± √(1-sin²(140°))
• ± 1/√(1 + tan²(140°))
• ± cot 140°/√(1 + cot²(140°))
• ± √(cosec²(140°) - 1)/cosec 140°
• 1/sec 140°

☛ Also check: trigonometric table

How to Find the Value of Cos 140 Degrees?

The value of cos 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 cos 140° is equal to the x-coordinate (-0.766). ∴ cos 140° = -0.766.

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

Since the cosine function can be represented using the cosecant function, we can write cos 140° as -[√(cosec²(140°) - 1)/cosec 140°]. The value of cosec 140° is equal to 1.55572.

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

Using trigonometric identities, we can write cos 140° in terms of sin 140° as, cos(140°) = -√(1 - sin²(140°)). Here, the value of sin 140° is equal to 0.6428.