Cos 1140 как найти

The value of cos 1140 degrees is 0.5. Cos 1140 degrees in radians is written as cos (1140° × π/180°), i.e., cos (19π/3) or cos (19.896753. . .). In this article, we will discuss the methods to find the value of cos 1140 degrees with examples.

• Cos 1140°: 0.5
• Cos 1140° in fraction: 1/2
• Cos (-1140 degrees): 0.5
• Cos 1140° in radians: cos (19π/3) or cos (19.8967534 . . .)

What is the Value of Cos 1140 Degrees?

The value of cos 1140 degrees in decimal is 0.5. Cos 1140 degrees can also be expressed using the equivalent of the given angle (1140 degrees) in radians (19.89675 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1140 degrees = 1140° × (π/180°) rad = 19π/3 or 19.8967 . . .
∴ cos 1140° = cos(19.8967) = 1/2 or 0.5

Explanation:

For cos 1140°, the angle 1140° > 360°. Given the periodic property of the cosine function, we can represent it as cos(1140° mod 360°) = cos(60°). The angle 1140°, coterminal to angle 60°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 1140 degrees value = 1/2 or 0.5
Similarly, cos 1140° can also be written as, cos 1140 degrees = (1140° + n × 360°), n ∈ Z.
⇒ cos 1140° = cos 1500° = cos 1860°, and so on.
Note: Since, cosine is an even function, the value of cos(-1140°) = cos(1140°).

Methods to Find Value of Cos 1140 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 1140° is given as 0.5. We can find the value of cos 1140 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 1140° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 1140 degrees as:

• ± √(1-sin²(1140°))
• ± 1/√(1 + tan²(1140°))
• ± cot 1140°/√(1 + cot²(1140°))
• ±√(cosec²(1140°) — 1)/cosec 1140°
• 1/sec 1140°

Note: Since 1140° lies in the 1st Quadrant, the final value of cos 1140° will be positive.

We can use trigonometric identities to represent cos 1140° as,

• -cos(180° — 1140°) = -cos(-960°)
• -cos(180° + 1140°) = -cos 1320°
• sin(90° + 1140°) = sin 1230°
• sin(90° — 1140°) = sin(-1050°)

Cos 1140 Degrees Using Unit Circle

To find the value of cos 1140 degrees using the unit circle, represent 1140° in the form (3 × 360°) + 60° [∵ 1140°>360°] ∵ cosine is a periodic function, cos 1140° = cos 60°.

• Rotate ‘r’ anticlockwise to form 60° or 1140° angle with the positive x-axis.
• The cos of 1140 degrees equals the x-coordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.

Hence the value of cos 1140° = x = 0.5

☛ Also Check:

• cos 90 degrees
• cos 11 degrees
• cos 30 degrees
• cos 16 degrees
• cos 56 degrees
• cos 5 degrees

FAQs on Cos 1140 Degrees

What is Cos 1140 Degrees?

Cos 1140 degrees is the value of cosine trigonometric function for an angle equal to 1140 degrees. The value of cos 1140° is 1/2 or 0.5

How to Find the Value of Cos 1140 Degrees?

The value of cos 1140 degrees can be calculated by constructing an angle of 1140° with the x-axis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos 1140° is equal to the x-coordinate (0.5). ∴ cos 1140° = 0.5.

What is the Exact Value of cos 1140 Degrees?

The exact value of cos 1140 degrees is 0.5.

What is the Value of Cos 1140 Degrees in Terms of Sin 1140°?

Using trigonometric identities, we can write cos 1140° in terms of sin 1140° as, cos(1140°) = √(1 — sin²(1140°)). Here, the value of sin 1140° is equal to 0.866.

How to Find Cos 1140° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 1140° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(1140°))
• ± 1/√(1 + tan²(1140°))
• ± cot 1140°/√(1 + cot²(1140°))
• ± √(cosec²(1140°) — 1)/cosec 1140°
• 1/sec 1140°

☛ Also check: trigonometry table