Cos 120 Degrees
The value of cos 120 degrees is 0.5. Cos 120 degrees in radians is written as cos (120° × π/180°), i.e., cos (2π/3) or cos (2.094395. . .). In this article, we will discuss the methods to find the value of cos 120 degrees with examples.
 Cos 120°: 0.5
 Cos 120° in fraction: (1/2)
 Cos (120 degrees): 0.5
 Cos 120° in radians: cos (2π/3) or cos (2.0943951 . . .)
What is the Value of Cos 120 Degrees?
The value of cos 120 degrees in decimal is 0.5. Cos 120 degrees can also be expressed using the equivalent of the given angle (120 degrees) in radians (2.09439 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 120 degrees = 120° × (π/180°) rad = 2π/3 or 2.0943 . . .
∴ cos 120° = cos(2.0943) = (1/2) or 0.5
Explanation:
For cos 120 degrees, the angle 120° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 120° value = (1/2) or 0.5
Since the cosine function is a periodic function, we can represent cos 120° as, cos 120 degrees = cos(120° + n × 360°), n ∈ Z.
⇒ cos 120° = cos 480° = cos 840°, and so on.
Note: Since, cosine is an even function, the value of cos(120°) = cos(120°).
Methods to Find Value of Cos 120 Degrees
The cosine function is negative in the 2nd quadrant. The value of cos 120° is given as 0.5. We can find the value of cos 120 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cos 120 Degrees Using Unit Circle
To find the value of cos 120 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 120° angle with the positive xaxis.
 The cos of 120 degrees equals the xcoordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.
Hence the value of cos 120° = x = 0.5
Cos 120° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 120 degrees as:
 ± √(1sin²(120°))
 ± 1/√(1 + tan²(120°))
 ± cot 120°/√(1 + cot²(120°))
 ±√(cosec²(120°)  1)/cosec 120°
 1/sec 120°
Note: Since 120° lies in the 2nd Quadrant, the final value of cos 120° will be negative.
We can use trigonometric identities to represent cos 120° as,
 cos(180°  120°) = cos 60°
 cos(180° + 120°) = cos 300°
 sin(90° + 120°) = sin 210°
 sin(90°  120°) = sin(30°)
☛ Also Check:
Examples Using Cos 120 Degrees

Example 1: Using the value of cos 120°, solve: (1sin²(120°)).
Solution:
We know, (1sin²(120°)) = (cos²(120°)) = 0.25
⇒ (1sin²(120°)) = 0.25 
Example 2: Find the value of 2 cos(120°)/3 sin(30°).
Solution:
Using trigonometric identities, we know, cos(120°) = sin(90°  120°) = sin(30°).
⇒ cos(120°) = sin(30°)
⇒ Value of 2 cos(120°)/3 sin(30°) = 2/3 
Example 3: Find the value of (cos² 60°  sin² 60°). [Hint: Use cos 120° = 0.5]
Solution:
Using the cos 2a formula,
(cos² 60°  sin² 60°) = cos(2 × 60°) = cos 120°
∵ cos 120° = 0.5
⇒ (cos² 60°  sin² 60°) = 0.5
FAQs on Cos 120 Degrees
What is Cos 120 Degrees?
Cos 120 degrees is the value of cosine trigonometric function for an angle equal to 120 degrees. The value of cos 120° is (1/2) or 0.5
What is the Value of Cos 120 Degrees in Terms of Tan 120°?
We know, using trig identities, we can write cos 120° as 1/√(1 + tan²(120°)). Here, the value of tan 120° is equal to 1.732050.
What is the Value of Cos 120° in Terms of Cosec 120°?
Since the cosine function can be represented using the cosecant function, we can write cos 120° as [√(cosec²(120°)  1)/cosec 120°]. The value of cosec 120° is equal to 1.15470.
How to Find Cos 120° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 120° can be given in terms of other trigonometric functions as:
 ± √(1sin²(120°))
 ± 1/√(1 + tan²(120°))
 ± cot 120°/√(1 + cot²(120°))
 ± √(cosec²(120°)  1)/cosec 120°
 1/sec 120°
☛ Also check: trigonometric table
How to Find the Value of Cos 120 Degrees?
The value of cos 120 degrees can be calculated by constructing an angle of 120° with the xaxis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos 120° is equal to the xcoordinate (0.5). ∴ cos 120° = 0.5.
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