Sin 210 Degrees

The value of sin 210 degrees is -0.5. Sin 210 degrees in radians is written as sin (210° × π/180°), i.e., sin (7π/6) or sin (3.665191. . .). In this article, we will discuss the methods to find the value of sin 210 degrees with examples.

• Sin 210°: -0.5
• Sin 210° in fraction: -(1/2)
• Sin (-210 degrees): 0.5
• Sin 210° in radians: sin (7π/6) or sin (3.6651914 . . .)

What is the Value of Sin 210 Degrees?

The value of sin 210 degrees in decimal is -0.5. Sin 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ sin 210° = sin(3.6651) = -(1/2) or -0.5

Explanation:

For sin 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 210° value = -(1/2) or -0.5
Since the sine function is a periodic function, we can represent sin 210° as, sin 210 degrees = sin(210° + n × 360°), n ∈ Z.
⇒ sin 210° = sin 570° = sin 930°, and so on.
Note: Since, sine is an odd function, the value of sin(-210°) = -sin(210°).

Methods to Find Value of Sin 210 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 210° is given as -0.5. We can find the value of sin 210 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 210 Degrees Using Unit Circle

To find the value of sin 210 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 210° angle with the positive x-axis.
• The sin of 210 degrees equals the y-coordinate(-0.5) of the point of intersection (-0.866, -0.5) of unit circle and r.

Hence the value of sin 210° = y = -0.5

Sin 210° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 210 degrees as:

• ± √(1-cos²(210°))
• ± tan 210°/√(1 + tan²(210°))
• ± 1/√(1 + cot²(210°))
• ± √(sec²(210°) - 1)/sec 210°
• 1/cosec 210°

Note: Since 210° lies in the 3rd Quadrant, the final value of sin 210° will be negative.

We can use trigonometric identities to represent sin 210° as,

• sin(180° - 210°) = sin(-30°)
• -sin(180° + 210°) = -sin 390°
• cos(90° - 210°) = cos(-120°)
• -cos(90° + 210°) = -cos 300°

☛ Also Check:

• sin 15 degrees
• sin 45 degrees
• sin 150 degrees
• sin 56 degrees
• sin 115 degrees
• sin 78 degrees

FAQs on Sin 210 Degrees

What is Sin 210 Degrees?

Sin 210 degrees is the value of sine trigonometric function for an angle equal to 210 degrees. The value of sin 210° is -(1/2) or -0.5.

How to Find the Value of Sin 210 Degrees?

The value of sin 210 degrees can be calculated by constructing an angle of 210° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, -0.5) on the unit circle. The value of sin 210° is equal to the y-coordinate (-0.5). ∴ sin 210° = -0.5.

What is the Exact Value of sin 210 Degrees?

The exact value of sin 210 degrees is -0.5.

What is the Value of Sin 210 Degrees in Terms of Cot 210°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 210° can be written as -1/√(1 + cot²(210°)). Here, the value of cot 210° is equal to 1.73205.

How to Find Sin 210° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 210° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(210°))
• ± tan 210°/√(1 + tan²(210°))
• ± 1/√(1 + cot²(210°))
• ± √(sec²(210°) - 1)/sec 210°
• 1/cosec 210°

☛ Also check: trigonometric table