Cos 11 Degrees

The value of cos 11 degrees is 0.9816271. . .. Cos 11 degrees in radians is written as cos (11° × π/180°), i.e., cos (0.191986. . .). In this article, we will discuss the methods to find the value of cos 11 degrees with examples.

• Cos 11°: 0.9816271. . .
• Cos (-11 degrees): 0.9816271. . .
• Cos 11° in radians: cos (0.1919862 . . .)

What is the Value of Cos 11 Degrees?

The value of cos 11 degrees in decimal is 0.981627183. . .. Cos 11 degrees can also be expressed using the equivalent of the given angle (11 degrees) in radians (0.19198 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 11 degrees = 11° × (π/180°) rad = 0.1919 . . .
∴ cos 11° = cos(0.1919) = 0.9816271. . .

Explanation:

For cos 11 degrees, the angle 11° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 11° value = 0.9816271. . .
Since the cosine function is a periodic function, we can represent cos 11° as, cos 11 degrees = cos(11° + n × 360°), n ∈ Z.
⇒ cos 11° = cos 371° = cos 731°, and so on.
Note: Since, cosine is an even function, the value of cos(-11°) = cos(11°).

Methods to Find Value of Cos 11 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 11° is given as 0.98162. . .. We can find the value of cos 11 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 11° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 11 degrees as:

• ± √(1-sin²(11°))
• ± 1/√(1 + tan²(11°))
• ± cot 11°/√(1 + cot²(11°))
• ±√(cosec²(11°) - 1)/cosec 11°
• 1/sec 11°

Note: Since 11° lies in the 1st Quadrant, the final value of cos 11° will be positive.

We can use trigonometric identities to represent cos 11° as,

• -cos(180° - 11°) = -cos 169°
• -cos(180° + 11°) = -cos 191°
• sin(90° + 11°) = sin 101°
• sin(90° - 11°) = sin 79°

Cos 11 Degrees Using Unit Circle

To find the value of cos 11 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 11° angle with the positive x-axis.
• The cos of 11 degrees equals the x-coordinate(0.9816) of the point of intersection (0.9816, 0.1908) of unit circle and r.

Hence the value of cos 11° = x = 0.9816 (approx)

☛ Also Check:

• cos 11 degrees
• cos 45 degrees
• cos 180 degrees
• cos 840 degrees
• cos 34 degrees
• cos 330 degrees

FAQs on Cos 11 Degrees

What is Cos 11 Degrees?

Cos 11 degrees is the value of cosine trigonometric function for an angle equal to 11 degrees. The value of cos 11° is 0.9816 (approx)

How to Find Cos 11° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 11° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(11°))
• ± 1/√(1 + tan²(11°))
• ± cot 11°/√(1 + cot²(11°))
• ± √(cosec²(11°) - 1)/cosec 11°
• 1/sec 11°

☛ Also check: trigonometry table

What is the Value of Cos 11 Degrees in Terms of Tan 11°?

We know, using trig identities, we can write cos 11° as 1/√(1 + tan²(11°)). Here, the value of tan 11° is equal to 0.194380.

What is the Exact Value of cos 11 Degrees?

The exact value of cos 11 degrees can be given accurately up to 8 decimal places as 0.98162718.

How to Find the Value of Cos 11 Degrees?

The value of cos 11 degrees can be calculated by constructing an angle of 11° with the x-axis, and then finding the coordinates of the corresponding point (0.9816, 0.1908) on the unit circle. The value of cos 11° is equal to the x-coordinate (0.9816). ∴ cos 11° = 0.9816.