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Cos 36 Degrees
The value of cos 36 degrees is 0.8090169. . .. Cos 36 degrees in radians is written as cos (36° × π/180°), i.e., cos (π/5) or cos (0.628318. . .). In this article, we will discuss the methods to find the value of cos 36 degrees with examples.
 Cos 36°: 0.8090169. . .
 Cos 36° in fraction: (1 + √5)/4
 Cos (36 degrees): 0.8090169. . .
 Cos 36° in radians: cos (π/5) or cos (0.6283185 . . .)
What is the Value of Cos 36 Degrees?
The value of cos 36 degrees in decimal is 0.809016994. . .. Cos 36 degrees can also be expressed using the equivalent of the given angle (36 degrees) in radians (0.62831 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 36 degrees = 36° × (π/180°) rad = π/5 or 0.6283 . . .
∴ cos 36° = cos(0.6283) = (1 + √5)/4 or 0.8090169. . .
Explanation:
For cos 36 degrees, the angle 36° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 36° value = (1 + √5)/4 or 0.8090169. . .
Since the cosine function is a periodic function, we can represent cos 36° as, cos 36 degrees = cos(36° + n × 360°), n ∈ Z.
⇒ cos 36° = cos 396° = cos 756°, and so on.
Note: Since, cosine is an even function, the value of cos(36°) = cos(36°).
Methods to Find Value of Cos 36 Degrees
The cosine function is positive in the 1st quadrant. The value of cos 36° is given as 0.80901. . .. We can find the value of cos 36 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Cos 36° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 36 degrees as:
 ± √(1sin²(36°))
 ± 1/√(1 + tan²(36°))
 ± cot 36°/√(1 + cot²(36°))
 ±√(cosec²(36°)  1)/cosec 36°
 1/sec 36°
Note: Since 36° lies in the 1st Quadrant, the final value of cos 36° will be positive.
We can use trigonometric identities to represent cos 36° as,
 cos(180°  36°) = cos 144°
 cos(180° + 36°) = cos 216°
 sin(90° + 36°) = sin 126°
 sin(90°  36°) = sin 54°
Cos 36 Degrees Using Unit Circle
To find the value of cos 36 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 36° angle with the positive xaxis.
 The cos of 36 degrees equals the xcoordinate(0.809) of the point of intersection (0.809, 0.5878) of unit circle and r.
Hence the value of cos 36° = x = 0.809 (approx)
☛ Also Check:
Examples Using Cos 36 Degrees

Example 1: Find the value of cos 36° if sec 36° is 1.2360.
Solution:
Since, cos 36° = 1/sec 36°
⇒ cos 36° = 1/1.2360 = 0.809 
Example 2: Find the value of 2 cos(36°)/3 sin(54°).
Solution:
Using trigonometric identities, we know, cos(36°) = sin(90°  36°) = sin 54°.
⇒ cos(36°) = sin(54°)
⇒ Value of 2 cos(36°)/3 sin(54°) = 2/3 
Example 3: Using the value of cos 36°, solve: (1sin²(36°)).
Solution:
We know, (1sin²(36°)) = (cos²(36°)) = 0.6545
⇒ (1sin²(36°)) = 0.6545
FAQs on Cos 36 Degrees
What is Cos 36 Degrees?
Cos 36 degrees is the value of cosine trigonometric function for an angle equal to 36 degrees. The value of cos 36° is (1 + √5)/4 or 0.809 (approx)
How to Find the Value of Cos 36 Degrees?
The value of cos 36 degrees can be calculated by constructing an angle of 36° with the xaxis, and then finding the coordinates of the corresponding point (0.809, 0.5878) on the unit circle. The value of cos 36° is equal to the xcoordinate (0.809). ∴ cos 36° = 0.809.
What is the Exact Value of cos 36 Degrees?
The exact value of cos 36 degrees can be given accurately up to 8 decimal places as 0.80901699 and (1 + √5)/4 in fraction.
What is the Value of Cos 36 Degrees in Terms of Sin 36°?
Using trigonometric identities, we can write cos 36° in terms of sin 36° as, cos(36°) = √(1  sin²(36°)). Here, the value of sin 36° is equal to √(10  2√5)/4.
How to Find Cos 36° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 36° can be given in terms of other trigonometric functions as:
 ± √(1sin²(36°))
 ± 1/√(1 + tan²(36°))
 ± cot 36°/√(1 + cot²(36°))
 ± √(cosec²(36°)  1)/cosec 36°
 1/sec 36°
☛ Also check: trigonometry table
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