Cos 2 Degrees

The value of cos 2 degrees is 0.9993908. . .. Cos 2 degrees in radians is written as cos (2° × π/180°), i.e., cos (π/90) or cos (0.034906. . .). In this article, we will discuss the methods to find the value of cos 2 degrees with examples.

• Cos 2°: 0.9993908. . .
• Cos (-2 degrees): 0.9993908. . .
• Cos 2° in radians: cos (π/90) or cos (0.0349065 . . .)

What is the Value of Cos 2 Degrees?

The value of cos 2 degrees in decimal is 0.999390827. . .. Cos 2 degrees can also be expressed using the equivalent of the given angle (2 degrees) in radians (0.03490 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 2 degrees = 2° × (π/180°) rad = π/90 or 0.0349 . . .
∴ cos 2° = cos(0.0349) = 0.9993908. . .

Explanation:

For cos 2 degrees, the angle 2° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 2° value = 0.9993908. . .
Since the cosine function is a periodic function, we can represent cos 2° as, cos 2 degrees = cos(2° + n × 360°), n ∈ Z.
⇒ cos 2° = cos 362° = cos 722°, and so on.
Note: Since, cosine is an even function, the value of cos(-2°) = cos(2°).

Methods to Find Value of Cos 2 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 2° is given as 0.99939. . .. We can find the value of cos 2 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 2 Degrees Using Unit Circle

To find the value of cos 2 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 2° angle with the positive x-axis.
• The cos of 2 degrees equals the x-coordinate(0.9994) of the point of intersection (0.9994, 0.0349) of unit circle and r.

Hence the value of cos 2° = x = 0.9994 (approx)

Cos 2° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 2 degrees as:

• ± √(1-sin²(2°))
• ± 1/√(1 + tan²(2°))
• ± cot 2°/√(1 + cot²(2°))
• ±√(cosec²(2°) - 1)/cosec 2°
• 1/sec 2°

Note: Since 2° lies in the 1st Quadrant, the final value of cos 2° will be positive.

We can use trigonometric identities to represent cos 2° as,

• -cos(180° - 2°) = -cos 178°
• -cos(180° + 2°) = -cos 182°
• sin(90° + 2°) = sin 92°
• sin(90° - 2°) = sin 88°

☛ Also Check:

• cos 11 degrees
• cos 60 degrees
• cos 135 degrees
• cos 585 degrees
• cos 145 degrees
• cos 67 degrees

FAQs on Cos 2 Degrees

What is Cos 2 Degrees?

Cos 2 degrees is the value of cosine trigonometric function for an angle equal to 2 degrees. The value of cos 2° is 0.9994 (approx)

What is the Exact Value of cos 2 Degrees?

The exact value of cos 2 degrees can be given accurately up to 8 decimal places as 0.99939082.

How to Find the Value of Cos 2 Degrees?

The value of cos 2 degrees can be calculated by constructing an angle of 2° with the x-axis, and then finding the coordinates of the corresponding point (0.9994, 0.0349) on the unit circle. The value of cos 2° is equal to the x-coordinate (0.9994). ∴ cos 2° = 0.9994.

What is the Value of Cos 2 Degrees in Terms of Cot 2°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 2° can be written as cot 2°/√(1 + cot²(2°)). Here, the value of cot 2° is equal to 28.63625.

How to Find Cos 2° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 2° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(2°))
• ± 1/√(1 + tan²(2°))
• ± cot 2°/√(1 + cot²(2°))
• ± √(cosec²(2°) - 1)/cosec 2°
• 1/sec 2°

☛ Also check: trigonometry table