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 xaxis.
 The cos of 140 degrees equals the xcoordinate(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:
 ± √(1sin²(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:
Examples Using Cos 140 Degrees

Example 1: Simplify: 7 (cos 140°/sin 230°)
Solution:
We know cos 140° = sin 230°
⇒ 7 cos 140°/sin 230° = 7 (cos 140°/cos 140°)
= 7(1) = 7 
Example 2: Find the value of (cos² 70°  sin² 70°). [Hint: Use cos 140° = 0.766]
Solution:
Using the cos 2a formula,
(cos² 70°  sin² 70°) = cos(2 × 70°) = cos 140°
∵ cos 140° = 0.766
⇒ (cos² 70°  sin² 70°) = 0.766 
Example 3: Find the value of 2 cos(140°)/3 sin(50°).
Solution:
Using trigonometric identities, we know, cos(140°) = sin(90°  140°) = sin(50°).
⇒ cos(140°) = sin(50°)
⇒ Value of 2 cos(140°)/3 sin(50°) = 2/3
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:
 ± √(1sin²(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 xaxis, 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 xcoordinate (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.
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