Cos 60 Degrees Exact Value

Cos sixty Degrees

The value of cos 60 degrees is 0.5. Cos sixty degrees in radians is written equally cos (60° × π/180°), i.e., cos (π/3) or cos (ane.047197. . .). In this article, we will discuss the methods to find the value of cos threescore degrees with examples.

Cos 60°: 0.5
Cos 60° in fraction: ane/2
Cos (-60 degrees): 0.five
Cos 60° in radians: cos (π/3) or cos (ane.0471975 . . .)

What is the Value of Cos 60 Degrees?

The value of cos 60 degrees in decimal is 0.five. Cos 60 degrees tin likewise exist 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 one.0471 . . .
∴ cos 60° = cos(1.0471) = ane/2 or 0.5

Cos 60 Degrees

Explanation:

For cos 60 degrees, the angle 60° lies between 0° and 90° (Starting time Quadrant). Since cosine office is positive in the first quadrant, thus cos lx° value = 1/2 or 0.five
Since the cosine function is a periodic role, nosotros can represent cos 60° equally, cos lx degrees = cos(threescore° + due north × 360°), north ∈ 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.five. We can detect the value of cos 60 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cos 60° in Terms of Trigonometric Functions

Using trigonometry formulas, nosotros can represent the cos sixty degrees every bit:

± √(i-sin²(60°))
± 1/√(1 + tan²(60°))
± cot threescore°/√(1 + cot²(60°))
±√(cosec²(60°) - 1)/cosec lx°
ane/sec lx°

Notation: Since 60° lies in the 1st Quadrant, the last value of cos threescore° will be positive.

We tin utilize trigonometric identities to represent cos 60° equally,

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

Cos sixty Degrees Using Unit Circle

value of cos 60

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

Rotate 'r' anticlockwise to form sixty° angle with the positive x-axis.
The cos of 60 degrees equals the 10-coordinate(0.5) of the indicate of intersection (0.five, 0.866) of unit circumvolve and r.

Hence the value of cos lx° = x = 0.five

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

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

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

± √(one-sin²(60°))
± i/√(1 + tan²(60°))
± cot threescore°/√(one + cot²(60°))
± √(cosec²(sixty°) - 1)/cosec threescore°
ane/sec threescore°

☛ Likewise bank check: trigonometric table

How to Discover the Value of Cos 60 Degrees?

The value of cos 60 degrees can be calculated by amalgam an angle of 60° with the x-axis, and so finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos 60° is equal to the 10-coordinate (0.5). ∴ cos 60° = 0.v.

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

We know, using trig identities, we tin can write cos lx° as i/√(1 + tan²(60°)). Here, the value of tan 60° is equal to i.732050.

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

Since the cosine function can be represented using the cosecant function, nosotros tin can write cos 60° as [√(cosec²(60°) - 1)/cosec lx°]. The value of cosec 60° is equal to ane.15470.