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 xaxis.
 The cos of 2 degrees equals the xcoordinate(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:
 ± √(1sin²(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:
Examples Using Cos 2 Degrees

Example 1: Find the value of 2 cos(2°)/3 sin(88°).
Solution:
Using trigonometric identities, we know, cos(2°) = sin(90°  2°) = sin 88°.
⇒ cos(2°) = sin(88°)
⇒ Value of 2 cos(2°)/3 sin(88°) = 2/3 
Example 2: Simplify: 4 (cos 2°/sin 92°)
Solution:
We know cos 2° = sin 92°
⇒ 4 cos 2°/sin 92° = 4 (cos 2°/cos 2°)
= 4(1) = 4 
Example 3: Find the value of (cos² 1°  sin² 1°). [Hint: Use cos 2° = 0.9994]
Solution:
Using the cos 2a formula,
(cos² 1°  sin² 1°) = cos(2 × 1°) = cos 2°
∵ cos 2° = 0.9994
⇒ (cos² 1°  sin² 1°) = 0.9994
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 xaxis, 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 xcoordinate (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:
 ± √(1sin²(2°))
 ± 1/√(1 + tan²(2°))
 ± cot 2°/√(1 + cot²(2°))
 ± √(cosec²(2°)  1)/cosec 2°
 1/sec 2°
☛ Also check: trigonometry table
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