Cos 300 Degrees

The value of cos 300 degrees is 0.5. Cos 300 degrees in radians is written as cos (300° × π/180°), i.e., cos (5π/3) or cos (5.235987. . .). In this article, we will discuss the methods to find the value of cos 300 degrees with examples.

• Cos 300°: 0.5
• Cos 300° in fraction: 1/2
• Cos (-300 degrees): 0.5
• Cos 300° in radians: cos (5π/3) or cos (5.2359877 . . .)

What is the Value of Cos 300 Degrees?

The value of cos 300 degrees in decimal is 0.5. Cos 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . .
∴ cos 300° = cos(5.2359) = 1/2 or 0.5

Explanation:

For cos 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 300° value = 1/2 or 0.5
Since the cosine function is a periodic function, we can represent cos 300° as, cos 300 degrees = cos(300° + n × 360°), n ∈ Z.
⇒ cos 300° = cos 660° = cos 1020°, and so on.
Note: Since, cosine is an even function, the value of cos(-300°) = cos(300°).

Methods to Find Value of Cos 300 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 300° is given as 0.5. We can find the value of cos 300 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 300 Degrees Using Unit Circle

To find the value of cos 300 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 300° angle with the positive x-axis.
• The cos of 300 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 300° = x = 0.5

Cos 300° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 300 degrees as:

• ± √(1-sin²(300°))
• ± 1/√(1 + tan²(300°))
• ± cot 300°/√(1 + cot²(300°))
• ±√(cosec²(300°) - 1)/cosec 300°
• 1/sec 300°

Note: Since 300° lies in the 4th Quadrant, the final value of cos 300° will be positive.

We can use trigonometric identities to represent cos 300° as,

• -cos(180° - 300°) = -cos(-120°)
• -cos(180° + 300°) = -cos 480°
• sin(90° + 300°) = sin 390°
• sin(90° - 300°) = sin(-210°)

☛ Also Check:

• cos 300 degrees
• cos 53 degrees
• cos 37 degrees
• cos 245 degrees
• cos 27 degrees
• cos 62 degrees

FAQs on Cos 300 Degrees

What is Cos 300 Degrees?

Cos 300 degrees is the value of cosine trigonometric function for an angle equal to 300 degrees. The value of cos 300° is 1/2 or 0.5

What is the Value of Cos 300 Degrees in Terms of Sin 300°?

Using trigonometric identities, we can write cos 300° in terms of sin 300° as, cos(300°) = √(1 - sin²(300°)). Here, the value of sin 300° is equal to -(√3/2).

What is the Exact Value of cos 300 Degrees?

The exact value of cos 300 degrees is 0.5.

How to Find Cos 300° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 300° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(300°))
• ± 1/√(1 + tan²(300°))
• ± cot 300°/√(1 + cot²(300°))
• ± √(cosec²(300°) - 1)/cosec 300°
• 1/sec 300°

☛ Also check: trigonometric table

How to Find the Value of Cos 300 Degrees?

The value of cos 300 degrees can be calculated by constructing an angle of 300° 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 300° is equal to the x-coordinate (0.5). ∴ cos 300° = 0.5.