Cos 4 Degrees

The value of cos 4 degrees is 0.9975640. . .. Cos 4 degrees in radians is written as cos (4° × π/180°), i.e., cos (π/45) or cos (0.069813. . .). In this article, we will discuss the methods to find the value of cos 4 degrees with examples.

• Cos 4°: 0.9975640. . .
• Cos (-4 degrees): 0.9975640. . .
• Cos 4° in radians: cos (π/45) or cos (0.0698131 . . .)

What is the Value of Cos 4 Degrees?

The value of cos 4 degrees in decimal is 0.997564050. . .. Cos 4 degrees can also be expressed using the equivalent of the given angle (4 degrees) in radians (0.06981 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 4 degrees = 4° × (π/180°) rad = π/45 or 0.0698 . . .
∴ cos 4° = cos(0.0698) = 0.9975640. . .

Explanation:

For cos 4 degrees, the angle 4° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 4° value = 0.9975640. . .
Since the cosine function is a periodic function, we can represent cos 4° as, cos 4 degrees = cos(4° + n × 360°), n ∈ Z.
⇒ cos 4° = cos 364° = cos 724°, and so on.
Note: Since, cosine is an even function, the value of cos(-4°) = cos(4°).

Methods to Find Value of Cos 4 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 4° is given as 0.99756. . .. We can find the value of cos 4 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 4 Degrees Using Unit Circle

To find the value of cos 4 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 4° angle with the positive x-axis.
• The cos of 4 degrees equals the x-coordinate(0.9976) of the point of intersection (0.9976, 0.0698) of unit circle and r.

Hence the value of cos 4° = x = 0.9976 (approx)

Cos 4° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 4 degrees as:

• ± √(1-sin²(4°))
• ± 1/√(1 + tan²(4°))
• ± cot 4°/√(1 + cot²(4°))
• ±√(cosec²(4°) - 1)/cosec 4°
• 1/sec 4°

Note: Since 4° lies in the 1st Quadrant, the final value of cos 4° will be positive.

We can use trigonometric identities to represent cos 4° as,

• -cos(180° - 4°) = -cos 176°
• -cos(180° + 4°) = -cos 184°
• sin(90° + 4°) = sin 94°
• sin(90° - 4°) = sin 86°

☛ Also Check:

• cos 210 degrees
• cos 11 degrees
• cos 240 degrees
• cos 5 degrees
• cos 115 degrees
• cos 77 degrees

FAQs on Cos 4 Degrees

What is Cos 4 Degrees?

Cos 4 degrees is the value of cosine trigonometric function for an angle equal to 4 degrees. The value of cos 4° is 0.9976 (approx)

What is the Value of Cos 4 Degrees in Terms of Sin 4°?

Using trigonometric identities, we can write cos 4° in terms of sin 4° as, cos(4°) = √(1 - sin²(4°)). Here, the value of sin 4° is equal to 0.0698.

How to Find Cos 4° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 4° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(4°))
• ± 1/√(1 + tan²(4°))
• ± cot 4°/√(1 + cot²(4°))
• ± √(cosec²(4°) - 1)/cosec 4°
• 1/sec 4°

☛ Also check: trigonometry table

What is the Value of Cos 4° in Terms of Cosec 4°?

Since the cosine function can be represented using the cosecant function, we can write cos 4° as [√(cosec²(4°) - 1)/cosec 4°]. The value of cosec 4° is equal to 14.33558.

How to Find the Value of Cos 4 Degrees?

The value of cos 4 degrees can be calculated by constructing an angle of 4° with the x-axis, and then finding the coordinates of the corresponding point (0.9976, 0.0698) on the unit circle. The value of cos 4° is equal to the x-coordinate (0.9976). ∴ cos 4° = 0.9976.