Cos 81 Degrees

The value of cos 81 degrees is 0.1564344. . .. Cos 81 degrees in radians is written as cos (81° × π/180°), i.e., cos (9π/20) or cos (1.413716. . .). In this article, we will discuss the methods to find the value of cos 81 degrees with examples.

• Cos 81°: 0.1564344. . .
• Cos (-81 degrees): 0.1564344. . .
• Cos 81° in radians: cos (9π/20) or cos (1.4137166 . . .)

What is the Value of Cos 81 Degrees?

The value of cos 81 degrees in decimal is 0.156434465. . .. Cos 81 degrees can also be expressed using the equivalent of the given angle (81 degrees) in radians (1.41371 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 81 degrees = 81° × (π/180°) rad = 9π/20 or 1.4137 . . .
∴ cos 81° = cos(1.4137) = 0.1564344. . .

Explanation:

For cos 81 degrees, the angle 81° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 81° value = 0.1564344. . .
Since the cosine function is a periodic function, we can represent cos 81° as, cos 81 degrees = cos(81° + n × 360°), n ∈ Z.
⇒ cos 81° = cos 441° = cos 801°, and so on.
Note: Since, cosine is an even function, the value of cos(-81°) = cos(81°).

Methods to Find Value of Cos 81 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 81° is given as 0.15643. . .. We can find the value of cos 81 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 81° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 81 degrees as:

• ± √(1-sin²(81°))
• ± 1/√(1 + tan²(81°))
• ± cot 81°/√(1 + cot²(81°))
• ±√(cosec²(81°) - 1)/cosec 81°
• 1/sec 81°

Note: Since 81° lies in the 1st Quadrant, the final value of cos 81° will be positive.

We can use trigonometric identities to represent cos 81° as,

• -cos(180° - 81°) = -cos 99°
• -cos(180° + 81°) = -cos 261°
• sin(90° + 81°) = sin 171°
• sin(90° - 81°) = sin 9°

Cos 81 Degrees Using Unit Circle

To find the value of cos 81 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 81° angle with the positive x-axis.
• The cos of 81 degrees equals the x-coordinate(0.1564) of the point of intersection (0.1564, 0.9877) of unit circle and r.

Hence the value of cos 81° = x = 0.1564 (approx)

☛ Also Check:

• cos 360 degrees
• cos 37 degrees
• cos 0 degrees
• cos 14 degrees
• cos 8 degrees
• cos 126 degrees

FAQs on Cos 81 Degrees

What is Cos 81 Degrees?

Cos 81 degrees is the value of cosine trigonometric function for an angle equal to 81 degrees. The value of cos 81° is 0.1564 (approx)

How to Find the Value of Cos 81 Degrees?

The value of cos 81 degrees can be calculated by constructing an angle of 81° with the x-axis, and then finding the coordinates of the corresponding point (0.1564, 0.9877) on the unit circle. The value of cos 81° is equal to the x-coordinate (0.1564). ∴ cos 81° = 0.1564.

What is the Value of Cos 81 Degrees in Terms of Tan 81°?

We know, using trig identities, we can write cos 81° as 1/√(1 + tan²(81°)). Here, the value of tan 81° is equal to 6.313751.

What is the Exact Value of cos 81 Degrees?

The exact value of cos 81 degrees can be given accurately up to 8 decimal places as 0.15643446.

How to Find Cos 81° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 81° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(81°))
• ± 1/√(1 + tan²(81°))
• ± cot 81°/√(1 + cot²(81°))
• ± √(cosec²(81°) - 1)/cosec 81°
• 1/sec 81°

☛ Also check: trigonometry table