Cos 240 Degrees

The value of cos 240 degrees is -0.5. Cos 240 degrees in radians is written as cos (240° × π/180°), i.e., cos (4π/3) or cos (4.188790. . .). In this article, we will discuss the methods to find the value of cos 240 degrees with examples.

• Cos 240°: -0.5
• Cos 240° in fraction: -(1/2)
• Cos (-240 degrees): -0.5
• Cos 240° in radians: cos (4π/3) or cos (4.1887902 . . .)

What is the Value of Cos 240 Degrees?

The value of cos 240 degrees in decimal is -0.5. Cos 240 degrees can also be expressed using the equivalent of the given angle (240 degrees) in radians (4.18879 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 240 degrees = 240° × (π/180°) rad = 4π/3 or 4.1887 . . .
∴ cos 240° = cos(4.1887) = -(1/2) or -0.5

Explanation:

For cos 240 degrees, the angle 240° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 240° value = -(1/2) or -0.5
Since the cosine function is a periodic function, we can represent cos 240° as, cos 240 degrees = cos(240° + n × 360°), n ∈ Z.
⇒ cos 240° = cos 600° = cos 960°, and so on.
Note: Since, cosine is an even function, the value of cos(-240°) = cos(240°).

Methods to Find Value of Cos 240 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 240° is given as -0.5. We can find the value of cos 240 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 240 Degrees Using Unit Circle

To find the value of cos 240 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 240° angle with the positive x-axis.
• The cos of 240 degrees equals the x-coordinate(-0.5) of the point of intersection (-0.5, -0.866) of unit circle and r.

Hence the value of cos 240° = x = -0.5

Cos 240° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 240 degrees as:

• ± √(1-sin²(240°))
• ± 1/√(1 + tan²(240°))
• ± cot 240°/√(1 + cot²(240°))
• ±√(cosec²(240°) - 1)/cosec 240°
• 1/sec 240°

Note: Since 240° lies in the 3rd Quadrant, the final value of cos 240° will be negative.

We can use trigonometric identities to represent cos 240° as,

• -cos(180° - 240°) = -cos(-60°)
• -cos(180° + 240°) = -cos 420°
• sin(90° + 240°) = sin 330°
• sin(90° - 240°) = sin(-150°)

☛ Also Check:

• cos 36 degrees
• cos 180 degrees
• cos 18 degrees
• cos 8 degrees
• cos 1080 degrees
• cos 105 degrees

FAQs on Cos 240 Degrees

What is Cos 240 Degrees?

Cos 240 degrees is the value of cosine trigonometric function for an angle equal to 240 degrees. The value of cos 240° is -(1/2) or -0.5

How to Find the Value of Cos 240 Degrees?

The value of cos 240 degrees can be calculated by constructing an angle of 240° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of cos 240° is equal to the x-coordinate (-0.5). ∴ cos 240° = -0.5.

How to Find Cos 240° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 240° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(240°))
• ± 1/√(1 + tan²(240°))
• ± cot 240°/√(1 + cot²(240°))
• ± √(cosec²(240°) - 1)/cosec 240°
• 1/sec 240°

☛ Also check: trigonometry table

What is the Value of Cos 240 Degrees in Terms of Tan 240°?

We know, using trig identities, we can write cos 240° as -1/√(1 + tan²(240°)). Here, the value of tan 240° is equal to 1.732050.

What is the Value of Cos 240° in Terms of Sec 240°?

Since the secant function is the reciprocal of the cosine function, we can write cos 240° as 1/sec(240°). The value of sec 240° is equal to -2.