Cos 60 Degrees

The value of cos 60 degrees is 0.5. Cos 60 degrees in radians is written as cos (60° × π/180°), i.e., cos (π/3) or cos (1.047197. . .). In this article, we will discuss the methods to find the value of cos 60 degrees with examples.

• Cos 60°: 0.5
• Cos 60° in fraction: 1/2
• Cos (-60 degrees): 0.5
• Cos 60° in radians: cos (π/3) or cos (1.0471975 . . .)

What is the Value of Cos 60 Degrees?

The value of cos 60 degrees in decimal is 0.5. Cos 60 degrees can also be expressed using the equivalent of the given angle (60 degrees) in radians (1.04719 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 60 degrees = 60° × (π/180°) rad = π/3 or 1.0471 . . .
∴ cos 60° = cos(1.0471) = 1/2 or 0.5

Explanation:

For cos 60 degrees, the angle 60° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 60° value = 1/2 or 0.5
Since the cosine function is a periodic function, we can represent cos 60° as, cos 60 degrees = cos(60° + n × 360°), n ∈ Z.
⇒ cos 60° = cos 420° = cos 780°, and so on.
Note: Since, cosine is an even function, the value of cos(-60°) = cos(60°).

Methods to Find Value of Cos 60 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 60° is given as 0.5. We can find the value of cos 60 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 60° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 60 degrees as:

• ± √(1-sin²(60°))
• ± 1/√(1 + tan²(60°))
• ± cot 60°/√(1 + cot²(60°))
• ±√(cosec²(60°) - 1)/cosec 60°
• 1/sec 60°

Note: Since 60° lies in the 1st Quadrant, the final value of cos 60° will be positive.

We can use trigonometric identities to represent cos 60° as,

• -cos(180° - 60°) = -cos 120°
• -cos(180° + 60°) = -cos 240°
• sin(90° + 60°) = sin 150°
• sin(90° - 60°) = sin 30°

Cos 60 Degrees Using Unit Circle

To find the value of cos 60 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 60° angle with the positive x-axis.
• The cos of 60 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 60° = x = 0.5

☛ Also Check:

• cos 240 degrees
• cos 45 degrees
• cos 270 degrees
• cos 24 degrees
• cos 765 degrees
• cos 100 degrees

FAQs on Cos 60 Degrees

What is Cos 60 Degrees?

Cos 60 degrees is the value of cosine trigonometric function for an angle equal to 60 degrees. The value of cos 60° is 1/2 or 0.5

How to Find Cos 60° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 60° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(60°))
• ± 1/√(1 + tan²(60°))
• ± cot 60°/√(1 + cot²(60°))
• ± √(cosec²(60°) - 1)/cosec 60°
• 1/sec 60°

☛ Also check: trigonometric table

How to Find the Value of Cos 60 Degrees?

The value of cos 60 degrees can be calculated by constructing an angle of 60° 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 60° is equal to the x-coordinate (0.5). ∴ cos 60° = 0.5.

What is the Value of Cos 60 Degrees in Terms of Tan 60°?

We know, using trig identities, we can write cos 60° as 1/√(1 + tan²(60°)). Here, the value of tan 60° is equal to 1.732050.

What is the Value of Cos 60° in Terms of Cosec 60°?

Since the cosine function can be represented using the cosecant function, we can write cos 60° as [√(cosec²(60°) - 1)/cosec 60°]. The value of cosec 60° is equal to 1.15470.