Sin 206 Degrees

The value of sin 206 degrees is -0.4383711. . .. Sin 206 degrees in radians is written as sin (206° × π/180°), i.e., sin (103π/90) or sin (3.595378. . .). In this article, we will discuss the methods to find the value of sin 206 degrees with examples.

• Sin 206°: -0.4383711. . .
• Sin (-206 degrees): 0.4383711. . .
• Sin 206° in radians: sin (103π/90) or sin (3.5953782 . . .)

What is the Value of Sin 206 Degrees?

The value of sin 206 degrees in decimal is -0.438371146. . .. Sin 206 degrees can also be expressed using the equivalent of the given angle (206 degrees) in radians (3.59537 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 206 degrees = 206° × (π/180°) rad = 103π/90 or 3.5953 . . .
∴ sin 206° = sin(3.5953) = -0.4383711. . .

Explanation:

For sin 206 degrees, the angle 206° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 206° value = -0.4383711. . .
Since the sine function is a periodic function, we can represent sin 206° as, sin 206 degrees = sin(206° + n × 360°), n ∈ Z.
⇒ sin 206° = sin 566° = sin 926°, and so on.
Note: Since, sine is an odd function, the value of sin(-206°) = -sin(206°).

Methods to Find Value of Sin 206 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 206° is given as -0.43837. . .. We can find the value of sin 206 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 206 Degrees Using Unit Circle

To find the value of sin 206 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 206° angle with the positive x-axis.
• The sin of 206 degrees equals the y-coordinate(-0.4384) of the point of intersection (-0.8988, -0.4384) of unit circle and r.

Hence the value of sin 206° = y = -0.4384 (approx)

Sin 206° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 206 degrees as:

• ± √(1-cos²(206°))
• ± tan 206°/√(1 + tan²(206°))
• ± 1/√(1 + cot²(206°))
• ± √(sec²(206°) - 1)/sec 206°
• 1/cosec 206°

Note: Since 206° lies in the 3rd Quadrant, the final value of sin 206° will be negative.

We can use trigonometric identities to represent sin 206° as,

• sin(180° - 206°) = sin(-26°)
• -sin(180° + 206°) = -sin 386°
• cos(90° - 206°) = cos(-116°)
• -cos(90° + 206°) = -cos 296°

☛ Also Check:

• sin 75 degrees
• sin 556 degrees
• sin 15 degrees
• sin 41 degrees
• sin 24 degrees
• sin 285 degrees

FAQs on Sin 206 Degrees

What is Sin 206 Degrees?

Sin 206 degrees is the value of sine trigonometric function for an angle equal to 206 degrees. The value of sin 206° is -0.4384 (approx).

What is the Value of Sin 206° in Terms of Cosec 206°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 206° as 1/cosec(206°). The value of cosec 206° is equal to -2.28117.

How to Find the Value of Sin 206 Degrees?

The value of sin 206 degrees can be calculated by constructing an angle of 206° with the x-axis, and then finding the coordinates of the corresponding point (-0.8988, -0.4384) on the unit circle. The value of sin 206° is equal to the y-coordinate (-0.4384). ∴ sin 206° = -0.4384.

How to Find Sin 206° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 206° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(206°))
• ± tan 206°/√(1 + tan²(206°))
• ± 1/√(1 + cot²(206°))
• ± √(sec²(206°) - 1)/sec 206°
• 1/cosec 206°

☛ Also check: trigonometry table

What is the Value of Sin 206 Degrees in Terms of Cot 206°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 206° can be written as -1/√(1 + cot²(206°)). Here, the value of cot 206° is equal to 2.05030.