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Cos 18 Degrees
The value of cos 18 degrees is 0.9510565. . .. Cos 18 degrees in radians is written as cos (18° × π/180°), i.e., cos (π/10) or cos (0.314159. . .). In this article, we will discuss the methods to find the value of cos 18 degrees with examples.
 Cos 18°: 0.9510565. . .
 Cos 18° in fraction: √(10 + 2√5)/4
 Cos (18 degrees): 0.9510565. . .
 Cos 18° in radians: cos (π/10) or cos (0.3141592 . . .)
What is the Value of Cos 18 Degrees?
The value of cos 18 degrees in decimal is 0.951056516. . .. Cos 18 degrees can also be expressed using the equivalent of the given angle (18 degrees) in radians (0.31415 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 18 degrees = 18° × (π/180°) rad = π/10 or 0.3141 . . .
∴ cos 18° = cos(0.3141) = √(10 + 2√5)/4 or 0.9510565. . .
Explanation:
For cos 18 degrees, the angle 18° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 18° value = √(10 + 2√5)/4 or 0.9510565. . .
Since the cosine function is a periodic function, we can represent cos 18° as, cos 18 degrees = cos(18° + n × 360°), n ∈ Z.
⇒ cos 18° = cos 378° = cos 738°, and so on.
Note: Since, cosine is an even function, the value of cos(18°) = cos(18°).
Methods to Find Value of Cos 18 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 18° is given as 0.95105. . .. We can find the value of cos 18 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cos 18 Degrees Using Unit Circle
To find the value of cos 18 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 18° angle with the positive xaxis.
 The cos of 18 degrees equals the xcoordinate(0.9511) of the point of intersection (0.9511, 0.309) of unit circle and r.
Hence the value of cos 18° = x = 0.9511 (approx)
Cos 18° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 18 degrees as:
 ± √(1sin²(18°))
 ± 1/√(1 + tan²(18°))
 ± cot 18°/√(1 + cot²(18°))
 ±√(cosec²(18°)  1)/cosec 18°
 1/sec 18°
Note: Since 18° lies in the 1st Quadrant, the final value of cos 18° will be positive.
We can use trigonometric identities to represent cos 18° as,
 cos(180°  18°) = cos 162°
 cos(180° + 18°) = cos 198°
 sin(90° + 18°) = sin 108°
 sin(90°  18°) = sin 72°
☛ Also Check:
Examples Using Cos 18 Degrees

Example 1: Find the value of (cos² 9°  sin² 9°). [Hint: Use cos 18° = 0.9511]
Solution:
Using the cos 2a formula,
(cos² 9°  sin² 9°) = cos(2 × 9°) = cos 18°
∵ cos 18° = 0.9511
⇒ (cos² 9°  sin² 9°) = 0.9511 
Example 2: Find the value of 2 cos(18°)/3 sin(72°).
Solution:
Using trigonometric identities, we know, cos(18°) = sin(90°  18°) = sin 72°.
⇒ cos(18°) = sin(72°)
⇒ Value of 2 cos(18°)/3 sin(72°) = 2/3 
Example 3: Find the value of cos 18° if sec 18° is 1.0514.
Solution:
Since, cos 18° = 1/sec 18°
⇒ cos 18° = 1/1.0514 = 0.9511
FAQs on Cos 18 Degrees
What is Cos 18 Degrees?
Cos 18 degrees is the value of cosine trigonometric function for an angle equal to 18 degrees. The value of cos 18° is √(10 + 2√5)/4 or 0.9511 (approx)
How to Find Cos 18° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 18° can be given in terms of other trigonometric functions as:
 ± √(1sin²(18°))
 ± 1/√(1 + tan²(18°))
 ± cot 18°/√(1 + cot²(18°))
 ± √(cosec²(18°)  1)/cosec 18°
 1/sec 18°
☛ Also check: trigonometry table
What is the Value of Cos 18 Degrees in Terms of Cot 18°?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 18° can be written as cot 18°/√(1 + cot²(18°)). Here, the value of cot 18° is equal to 3.07768.
How to Find the Value of Cos 18 Degrees?
The value of cos 18 degrees can be calculated by constructing an angle of 18° with the xaxis, and then finding the coordinates of the corresponding point (0.9511, 0.309) on the unit circle. The value of cos 18° is equal to the xcoordinate (0.9511). ∴ cos 18° = 0.9511.
What is the Exact Value of cos 18 Degrees?
The exact value of cos 18 degrees can be given accurately up to 8 decimal places as 0.95105651 and √(10 + 2√5)/4 in fraction.
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