# Cos 20 Cos 100 Cos 140

Cos 20 Cos 100 Cos 140.

## 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 (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°), tepi langit ∈ 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
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## 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.

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### 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.

## Cos 20 Cos 100 Cos 140

Source: https://www.cuemath.com/trigonometry/cos-140-degrees/

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