Sin 930 Degrees

The value of sin 930 degrees is -0.5. Sin 930 degrees in radians is written as sin (930° × π/180°), i.e., sin (31π/6) or sin (16.231562. . .). In this article, we will discuss the methods to find the value of sin 930 degrees with examples.

• Sin 930°: -0.5
• Sin 930° in fraction: -(1/2)
• Sin (-930 degrees): 0.5
• Sin 930° in radians: sin (31π/6) or sin (16.2315620 . . .)

What is the Value of Sin 930 Degrees?

The value of sin 930 degrees in decimal is -0.5. Sin 930 degrees can also be expressed using the equivalent of the given angle (930 degrees) in radians (16.23156 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 930 degrees = 930° × (π/180°) rad = 31π/6 or 16.2315 . . .
∴ sin 930° = sin(16.2315) = -(1/2) or -0.5

Explanation:

For sin 930°, the angle 930° > 360°. Given the periodic property of the sine function, we can represent it as sin(930° mod 360°) = sin(210°). The angle 930°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 930 degrees value = -(1/2) or -0.5
Similarly, sin 930° can also be written as, sin 930 degrees = (930° + n × 360°), n ∈ Z.
⇒ sin 930° = sin 1290° = sin 1650°, and so on.
Note: Since, sine is an odd function, the value of sin(-930°) = -sin(930°).

Methods to Find Value of Sin 930 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 930° is given as -0.5. We can find the value of sin 930 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 930 Degrees Using Unit Circle

To find the value of sin 930 degrees using the unit circle, represent 930° in the form (2 × 360°) + 210° [∵ 930°>360°] ∵ sine is a periodic function, sin 930° = sin 210°.

• Rotate ‘r’ anticlockwise to form a 210° or 930° angle with the positive x-axis.
• The sin of 930 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 930° = y = -0.5

Sin 930° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 930 degrees as:

• ± √(1-cos²(930°))
• ± tan 930°/√(1 + tan²(930°))
• ± 1/√(1 + cot²(930°))
• ± √(sec²(930°) - 1)/sec 930°
• 1/cosec 930°

Note: Since 930° lies in the 3rd Quadrant, the final value of sin 930° will be negative.

We can use trigonometric identities to represent sin 930° as,

• sin(180° - 930°) = sin(-750°)
• -sin(180° + 930°) = -sin 1110°
• cos(90° - 930°) = cos(-840°)
• -cos(90° + 930°) = -cos 1020°

☛ Also Check:

• sin 15 degrees
• sin 60 degrees
• sin 50 degrees
• sin 69 degrees
• sin 165 degrees
• sin 57 degrees

FAQs on Sin 930 Degrees

What is Sin 930 Degrees?

Sin 930 degrees is the value of sine trigonometric function for an angle equal to 930 degrees. The value of sin 930° is -(1/2) or -0.5.

What is the Value of Sin 930 Degrees in Terms of Cos 930°?

Using trigonometric identities, we can write sin 930° in terms of cos 930° as, sin(930°) = -√(1-cos²(930°)). Here, the value of cos 930° is equal to -0.8660254.

What is the Value of Sin 930° in Terms of Cosec 930°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 930° as 1/cosec(930°). The value of cosec 930° is equal to -2.

How to Find Sin 930° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 930° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(930°))
• ± tan 930°/√(1 + tan²(930°))
• ± 1/√(1 + cot²(930°))
• ± √(sec²(930°) - 1)/sec 930°
• 1/cosec 930°

☛ Also check: trigonometry table

How to Find the Value of Sin 930 Degrees?

The value of sin 930 degrees can be calculated by constructing an angle of 930° 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 930° is equal to the y-coordinate (-0.5). ∴ sin 930° = -0.5.