Sin 220 Degrees

The value of sin 220 degrees is -0.6427876. . .. Sin 220 degrees in radians is written as sin (220° × π/180°), i.e., sin (11π/9) or sin (3.839724. . .). In this article, we will discuss the methods to find the value of sin 220 degrees with examples.

• Sin 220°: -0.6427876. . .
• Sin (-220 degrees): 0.6427876. . .
• Sin 220° in radians: sin (11π/9) or sin (3.8397243 . . .)

What is the Value of Sin 220 Degrees?

The value of sin 220 degrees in decimal is -0.642787609. . .. Sin 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 . . .
∴ sin 220° = sin(3.8397) = -0.6427876. . .

Explanation:

For sin 220 degrees, the angle 220° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 220° value = -0.6427876. . .
Since the sine function is a periodic function, we can represent sin 220° as, sin 220 degrees = sin(220° + n × 360°), n ∈ Z.
⇒ sin 220° = sin 580° = sin 940°, and so on.
Note: Since, sine is an odd function, the value of sin(-220°) = -sin(220°).

Methods to Find Value of Sin 220 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 220° is given as -0.64278. . .. We can find the value of sin 220 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 220 Degrees Using Unit Circle

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

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

Hence the value of sin 220° = y = -0.6428 (approx)

Sin 220° in Terms of Trigonometric Functions

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

• ± √(1-cos²(220°))
• ± tan 220°/√(1 + tan²(220°))
• ± 1/√(1 + cot²(220°))
• ± √(sec²(220°) - 1)/sec 220°
• 1/cosec 220°

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

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

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

☛ Also Check:

• sin 35 degrees
• sin 15 degrees
• sin 36 degrees
• sin 71 degrees
• sin 33 degrees
• sin 933 degrees

FAQs on Sin 220 Degrees

What is Sin 220 Degrees?

Sin 220 degrees is the value of sine trigonometric function for an angle equal to 220 degrees. The value of sin 220° is -0.6428 (approx).

What is the Exact Value of sin 220 Degrees?

The exact value of sin 220 degrees can be given accurately up to 8 decimal places as -0.64278760.

How to Find the Value of Sin 220 Degrees?

The value of sin 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 sin 220° is equal to the y-coordinate (-0.6428). ∴ sin 220° = -0.6428.

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

Using trigonometric identities, we can write sin 220° in terms of cos 220° as, sin(220°) = -√(1-cos²(220°)). Here, the value of cos 220° is equal to -0.7660444.

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

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

• ± √(1-cos²(220°))
• ± tan 220°/√(1 + tan²(220°))
• ± 1/√(1 + cot²(220°))
• ± √(sec²(220°) - 1)/sec 220°
• 1/cosec 220°

☛ Also check: trigonometric table