Cos 220 Degrees

The value of cos 220 degrees is -0.7660444. . .. Cos 220 degrees in radians is written as cos (220° × π/180°), i.e., cos (11π/9) or cos (3.839724. . .). In this article, we will discuss the methods to find the value of cos 220 degrees with examples.

• Cos 220°: -0.7660444. . .
• Cos (-220 degrees): -0.7660444. . .
• Cos 220° in radians: cos (11π/9) or cos (3.8397243 . . .)

What is the Value of Cos 220 Degrees?

The value of cos 220 degrees in decimal is -0.766044443. . .. Cos 220 degrees can also be expressed using the equivalent of the given angle (220 degrees) in radians (3.83972 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 220 degrees = 220° × (π/180°) rad = 11π/9 or 3.8397 . . .
∴ cos 220° = cos(3.8397) = -0.7660444. . .

Explanation:

For cos 220 degrees, the angle 220° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 220° value = -0.7660444. . .
Since the cosine function is a periodic function, we can represent cos 220° as, cos 220 degrees = cos(220° + n × 360°), n ∈ Z.
⇒ cos 220° = cos 580° = cos 940°, and so on.
Note: Since, cosine is an even function, the value of cos(-220°) = cos(220°).

Methods to Find Value of Cos 220 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 220° is given as -0.76604. . .. We can find the value of cos 220 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 220° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 220 degrees as:

• ± √(1-sin²(220°))
• ± 1/√(1 + tan²(220°))
• ± cot 220°/√(1 + cot²(220°))
• ±√(cosec²(220°) - 1)/cosec 220°
• 1/sec 220°

Note: Since 220° lies in the 3rd Quadrant, the final value of cos 220° will be negative.

We can use trigonometric identities to represent cos 220° as,

• -cos(180° - 220°) = -cos(-40°)
• -cos(180° + 220°) = -cos 400°
• sin(90° + 220°) = sin 310°
• sin(90° - 220°) = sin(-130°)

Cos 220 Degrees Using Unit Circle

To find the value of cos 220 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 220° angle with the positive x-axis.
• The cos of 220 degrees equals the x-coordinate(-0.766) of the point of intersection (-0.766, -0.6428) of unit circle and r.

Hence the value of cos 220° = x = -0.766 (approx)

☛ Also Check:

• cos 60 degrees
• cos 75 degrees
• cos 18 degrees
• cos 28 degrees
• cos 85 degrees
• cos 540 degrees

FAQs on Cos 220 Degrees

What is Cos 220 Degrees?

Cos 220 degrees is the value of cosine trigonometric function for an angle equal to 220 degrees. The value of cos 220° is -0.766 (approx)

How to Find the Value of Cos 220 Degrees?

The value of cos 220 degrees can be calculated by constructing an angle of 220° with the x-axis, and then finding the coordinates of the corresponding point (-0.766, -0.6428) on the unit circle. The value of cos 220° is equal to the x-coordinate (-0.766). ∴ cos 220° = -0.766.

How to Find Cos 220° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 220° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(220°))
• ± 1/√(1 + tan²(220°))
• ± cot 220°/√(1 + cot²(220°))
• ± √(cosec²(220°) - 1)/cosec 220°
• 1/sec 220°

☛ Also check: trigonometric table

What is the Value of Cos 220° in Terms of Sec 220°?

Since the secant function is the reciprocal of the cosine function, we can write cos 220° as 1/sec(220°). The value of sec 220° is equal to -1.305407.

What is the Value of Cos 220 Degrees in Terms of Sin 220°?

Using trigonometric identities, we can write cos 220° in terms of sin 220° as, cos(220°) = -√(1 - sin²(220°)). Here, the value of sin 220° is equal to -0.6428.