Cos 72 Degrees

The value of cos 72 degrees is 0.3090169. . .. Cos 72 degrees in radians is written as cos (72° × π/180°), i.e., cos (2π/5) or cos (1.256637. . .). In this article, we will discuss the methods to find the value of cos 72 degrees with examples.

• Cos 72°: 0.3090169. . .
• Cos 72° in fraction: (√5 - 1)/4
• Cos (-72 degrees): 0.3090169. . .
• Cos 72° in radians: cos (2π/5) or cos (1.2566370 . . .)

What is the Value of Cos 72 Degrees?

The value of cos 72 degrees in decimal is 0.309016994. . .. Cos 72 degrees can also be expressed using the equivalent of the given angle (72 degrees) in radians (1.25663 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 72 degrees = 72° × (π/180°) rad = 2π/5 or 1.2566 . . .
∴ cos 72° = cos(1.2566) = (√5 - 1)/4 or 0.3090169. . .

Explanation:

For cos 72 degrees, the angle 72° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 72° value = (√5 - 1)/4 or 0.3090169. . .
Since the cosine function is a periodic function, we can represent cos 72° as, cos 72 degrees = cos(72° + n × 360°), n ∈ Z.
⇒ cos 72° = cos 432° = cos 792°, and so on.
Note: Since, cosine is an even function, the value of cos(-72°) = cos(72°).

Methods to Find Value of Cos 72 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 72° is given as 0.30901. . .. We can find the value of cos 72 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 72 Degrees Using Unit Circle

To find the value of cos 72 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 72° angle with the positive x-axis.
• The cos of 72 degrees equals the x-coordinate(0.309) of the point of intersection (0.309, 0.9511) of unit circle and r.

Hence the value of cos 72° = x = 0.309 (approx)

Cos 72° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 72 degrees as:

• ± √(1-sin²(72°))
• ± 1/√(1 + tan²(72°))
• ± cot 72°/√(1 + cot²(72°))
• ±√(cosec²(72°) - 1)/cosec 72°
• 1/sec 72°

Note: Since 72° lies in the 1st Quadrant, the final value of cos 72° will be positive.

We can use trigonometric identities to represent cos 72° as,

• -cos(180° - 72°) = -cos 108°
• -cos(180° + 72°) = -cos 252°
• sin(90° + 72°) = sin 162°
• sin(90° - 72°) = sin 18°

☛ Also Check:

• cos 21 degrees
• cos 210 degrees
• cos 3 degrees
• cos 28 degrees
• cos 200 degrees
• cos 280 degrees

FAQs on Cos 72 Degrees

What is Cos 72 Degrees?

Cos 72 degrees is the value of cosine trigonometric function for an angle equal to 72 degrees. The value of cos 72° is (√5 - 1)/4 or 0.309 (approx)

How to Find Cos 72° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 72° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(72°))
• ± 1/√(1 + tan²(72°))
• ± cot 72°/√(1 + cot²(72°))
• ± √(cosec²(72°) - 1)/cosec 72°
• 1/sec 72°

☛ Also check: trigonometric table

What is the Value of Cos 72 Degrees in Terms of Sin 72°?

Using trigonometric identities, we can write cos 72° in terms of sin 72° as, cos(72°) = √(1 - sin²(72°)). Here, the value of sin 72° is equal to √(10 - 2√5)/2.

What is the Exact Value of cos 72 Degrees?

The exact value of cos 72 degrees can be given accurately up to 8 decimal places as 0.30901699 and (√5 - 1)/4 in fraction.

How to Find the Value of Cos 72 Degrees?

The value of cos 72 degrees can be calculated by constructing an angle of 72° with the x-axis, and then finding the coordinates of the corresponding point (0.309, 0.9511) on the unit circle. The value of cos 72° is equal to the x-coordinate (0.309). ∴ cos 72° = 0.309.