Sin 200 Degrees

The value of sin 200 degrees is -0.3420201. . .. Sin 200 degrees in radians is written as sin (200° × π/180°), i.e., sin (10π/9) or sin (3.490658. . .). In this article, we will discuss the methods to find the value of sin 200 degrees with examples.

• Sin 200°: -0.3420201. . .
• Sin (-200 degrees): 0.3420201. . .
• Sin 200° in radians: sin (10π/9) or sin (3.4906585 . . .)

What is the Value of Sin 200 Degrees?

The value of sin 200 degrees in decimal is -0.342020143. . .. Sin 200 degrees can also be expressed using the equivalent of the given angle (200 degrees) in radians (3.49065 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 200 degrees = 200° × (π/180°) rad = 10π/9 or 3.4906 . . .
∴ sin 200° = sin(3.4906) = -0.3420201. . .

Explanation:

For sin 200 degrees, the angle 200° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 200° value = -0.3420201. . .
Since the sine function is a periodic function, we can represent sin 200° as, sin 200 degrees = sin(200° + n × 360°), n ∈ Z.
⇒ sin 200° = sin 560° = sin 920°, and so on.
Note: Since, sine is an odd function, the value of sin(-200°) = -sin(200°).

Methods to Find Value of Sin 200 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 200° is given as -0.34202. . .. We can find the value of sin 200 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 200 Degrees Using Unit Circle

To find the value of sin 200 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 200° angle with the positive x-axis.
• The sin of 200 degrees equals the y-coordinate(-0.342) of the point of intersection (-0.9397, -0.342) of unit circle and r.

Hence the value of sin 200° = y = -0.342 (approx)

Sin 200° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 200 degrees as:

• ± √(1-cos²(200°))
• ± tan 200°/√(1 + tan²(200°))
• ± 1/√(1 + cot²(200°))
• ± √(sec²(200°) - 1)/sec 200°
• 1/cosec 200°

Note: Since 200° lies in the 3rd Quadrant, the final value of sin 200° will be negative.

We can use trigonometric identities to represent sin 200° as,

• sin(180° - 200°) = sin(-20°)
• -sin(180° + 200°) = -sin 380°
• cos(90° - 200°) = cos(-110°)
• -cos(90° + 200°) = -cos 290°

☛ Also Check:

• sin 3 degrees
• sin 35 degrees
• sin 15 degrees
• sin 220 degrees
• sin 8 degrees
• sin 585 degrees

FAQs on Sin 200 Degrees

What is Sin 200 Degrees?

Sin 200 degrees is the value of sine trigonometric function for an angle equal to 200 degrees. The value of sin 200° is -0.342 (approx).

How to Find Sin 200° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 200° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(200°))
• ± tan 200°/√(1 + tan²(200°))
• ± 1/√(1 + cot²(200°))
• ± √(sec²(200°) - 1)/sec 200°
• 1/cosec 200°

☛ Also check: trigonometry table

What is the Exact Value of sin 200 Degrees?

The exact value of sin 200 degrees can be given accurately up to 8 decimal places as -0.34202014.

What is the Value of Sin 200 Degrees in Terms of Cos 200°?

Using trigonometric identities, we can write sin 200° in terms of cos 200° as, sin(200°) = -√(1-cos²(200°)). Here, the value of cos 200° is equal to -0.9396926.

How to Find the Value of Sin 200 Degrees?

The value of sin 200 degrees can be calculated by constructing an angle of 200° with the x-axis, and then finding the coordinates of the corresponding point (-0.9397, -0.342) on the unit circle. The value of sin 200° is equal to the y-coordinate (-0.342). ∴ sin 200° = -0.342.