Cos 1110 Degrees

The value of cos 1110 degrees is 0.8660254. . .. Cos 1110 degrees in radians is written as cos (1110° × π/180°), i.e., cos (37π/6) or cos (19.373154. . .). In this article, we will discuss the methods to find the value of cos 1110 degrees with examples.

• Cos 1110°: 0.8660254. . .
• Cos 1110° in fraction: √3/2
• Cos (-1110 degrees): 0.8660254. . .
• Cos 1110° in radians: cos (37π/6) or cos (19.3731546 . . .)

What is the Value of Cos 1110 Degrees?

The value of cos 1110 degrees in decimal is 0.866025403. . .. Cos 1110 degrees can also be expressed using the equivalent of the given angle (1110 degrees) in radians (19.37315 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1110 degrees = 1110° × (π/180°) rad = 37π/6 or 19.3731 . . .
∴ cos 1110° = cos(19.3731) = √3/2 or 0.8660254. . .

Explanation:

For cos 1110°, the angle 1110° > 360°. Given the periodic property of the cosine function, we can represent it as cos(1110° mod 360°) = cos(30°). The angle 1110°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 1110 degrees value = √3/2 or 0.8660254. . .
Similarly, cos 1110° can also be written as, cos 1110 degrees = (1110° + n × 360°), n ∈ Z.
⇒ cos 1110° = cos 1470° = cos 1830°, and so on.
Note: Since, cosine is an even function, the value of cos(-1110°) = cos(1110°).

Methods to Find Value of Cos 1110 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 1110° is given as 0.86602. . .. We can find the value of cos 1110 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 1110 Degrees Using Unit Circle

To find the value of cos 1110 degrees using the unit circle, represent 1110° in the form (3 × 360°) + 30° [∵ 1110°>360°] ∵ cosine is a periodic function, cos 1110° = cos 30°.

• Rotate ‘r’ anticlockwise to form 30° or 1110° angle with the positive x-axis.
• The cos of 1110 degrees equals the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of cos 1110° = x = 0.866 (approx)

Cos 1110° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 1110 degrees as:

• ± √(1-sin²(1110°))
• ± 1/√(1 + tan²(1110°))
• ± cot 1110°/√(1 + cot²(1110°))
• ±√(cosec²(1110°) - 1)/cosec 1110°
• 1/sec 1110°

Note: Since 1110° lies in the 1st Quadrant, the final value of cos 1110° will be positive.

We can use trigonometric identities to represent cos 1110° as,

• -cos(180° - 1110°) = -cos(-930°)
• -cos(180° + 1110°) = -cos 1290°
• sin(90° + 1110°) = sin 1200°
• sin(90° - 1110°) = sin(-1020°)

☛ Also Check:

• cos 30 degrees
• cos 11 degrees
• cos 60 degrees
• cos 48 degrees
• cos 71 degrees
• cos 420 degrees

FAQs on Cos 1110 Degrees

What is Cos 1110 Degrees?

Cos 1110 degrees is the value of cosine trigonometric function for an angle equal to 1110 degrees. The value of cos 1110° is √3/2 or 0.866 (approx)

How to Find the Value of Cos 1110 Degrees?

The value of cos 1110 degrees can be calculated by constructing an angle of 1110° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of cos 1110° is equal to the x-coordinate (0.866). ∴ cos 1110° = 0.866.

What is the Exact Value of cos 1110 Degrees?

The exact value of cos 1110 degrees can be given accurately up to 8 decimal places as 0.86602540 and √3/2 in fraction.

How to Find Cos 1110° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 1110° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(1110°))
• ± 1/√(1 + tan²(1110°))
• ± cot 1110°/√(1 + cot²(1110°))
• ± √(cosec²(1110°) - 1)/cosec 1110°
• 1/sec 1110°

☛ Also check: trigonometric table

What is the Value of Cos 1110 Degrees in Terms of Sin 1110°?

Using trigonometric identities, we can write cos 1110° in terms of sin 1110° as, cos(1110°) = √(1 - sin²(1110°)). Here, the value of sin 1110° is equal to 0.5.