Sin 330 Degrees

The value of sin 330 degrees is -0.5. Sin 330 degrees in radians is written as sin (330° × π/180°), i.e., sin (11π/6) or sin (5.759586. . .). In this article, we will discuss the methods to find the value of sin 330 degrees with examples.

• Sin 330°: -0.5
• Sin 330° in fraction: -(1/2)
• Sin (-330 degrees): 0.5
• Sin 330° in radians: sin (11π/6) or sin (5.7595865 . . .)

What is the Value of Sin 330 Degrees?

The value of sin 330 degrees in decimal is -0.5. Sin 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ sin 330° = sin(5.7595) = -(1/2) or -0.5

Explanation:

For sin 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 330° value = -(1/2) or -0.5
Since the sine function is a periodic function, we can represent sin 330° as, sin 330 degrees = sin(330° + n × 360°), n ∈ Z.
⇒ sin 330° = sin 690° = sin 1050°, and so on.
Note: Since, sine is an odd function, the value of sin(-330°) = -sin(330°).

Methods to Find Value of Sin 330 Degrees

The sine function is negative in the 4th quadrant. The value of sin 330° is given as -0.5. We can find the value of sin 330 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 330 Degrees Using Unit Circle

To find the value of sin 330 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 330° angle with the positive x-axis.
• The sin of 330 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 330° = y = -0.5

Sin 330° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 330 degrees as:

• ± √(1-cos²(330°))
• ± tan 330°/√(1 + tan²(330°))
• ± 1/√(1 + cot²(330°))
• ± √(sec²(330°) - 1)/sec 330°
• 1/cosec 330°

Note: Since 330° lies in the 4th Quadrant, the final value of sin 330° will be negative.

We can use trigonometric identities to represent sin 330° as,

• sin(180° - 330°) = sin(-150°)
• -sin(180° + 330°) = -sin 510°
• cos(90° - 330°) = cos(-240°)
• -cos(90° + 330°) = -cos 420°

☛ Also Check:

• sin 45 degrees
• sin 37 degrees
• sin 50 degrees
• sin 910 degrees
• sin 720 degrees
• sin 660 degrees

FAQs on Sin 330 Degrees

What is Sin 330 Degrees?

Sin 330 degrees is the value of sine trigonometric function for an angle equal to 330 degrees. The value of sin 330° is -(1/2) or -0.5.

What is the Exact Value of sin 330 Degrees?

The exact value of sin 330 degrees is -0.5.

How to Find Sin 330° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 330° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(330°))
• ± tan 330°/√(1 + tan²(330°))
• ± 1/√(1 + cot²(330°))
• ± √(sec²(330°) - 1)/sec 330°
• 1/cosec 330°

☛ Also check: trigonometric table

How to Find the Value of Sin 330 Degrees?

The value of sin 330 degrees can be calculated by constructing an angle of 330° 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 330° is equal to the y-coordinate (-0.5). ∴ sin 330° = -0.5.

What is the Value of Sin 330 Degrees in Terms of Cos 330°?

Using trigonometric identities, we can write sin 330° in terms of cos 330° as, sin(330°) = -√(1-cos²(330°)). Here, the value of cos 330° is equal to √3/2.