Sin 230 Degrees

The value of sin 230 degrees is -0.7660444. . .. Sin 230 degrees in radians is written as sin (230° × π/180°), i.e., sin (23π/18) or sin (4.014257. . .). In this article, we will discuss the methods to find the value of sin 230 degrees with examples.

• Sin 230°: -0.7660444. . .
• Sin (-230 degrees): 0.7660444. . .
• Sin 230° in radians: sin (23π/18) or sin (4.0142572 . . .)

What is the Value of Sin 230 Degrees?

The value of sin 230 degrees in decimal is -0.766044443. . .. Sin 230 degrees can also be expressed using the equivalent of the given angle (230 degrees) in radians (4.01425 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 230 degrees = 230° × (π/180°) rad = 23π/18 or 4.0142 . . .
∴ sin 230° = sin(4.0142) = -0.7660444. . .

Explanation:

For sin 230 degrees, the angle 230° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 230° value = -0.7660444. . .
Since the sine function is a periodic function, we can represent sin 230° as, sin 230 degrees = sin(230° + n × 360°), n ∈ Z.
⇒ sin 230° = sin 590° = sin 950°, and so on.
Note: Since, sine is an odd function, the value of sin(-230°) = -sin(230°).

Methods to Find Value of Sin 230 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 230° is given as -0.76604. . .. We can find the value of sin 230 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 230 Degrees Using Unit Circle

To find the value of sin 230 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 230° angle with the positive x-axis.
• The sin of 230 degrees equals the y-coordinate(-0.766) of the point of intersection (-0.6428, -0.766) of unit circle and r.

Hence the value of sin 230° = y = -0.766 (approx)

Sin 230° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 230 degrees as:

• ± √(1-cos²(230°))
• ± tan 230°/√(1 + tan²(230°))
• ± 1/√(1 + cot²(230°))
• ± √(sec²(230°) - 1)/sec 230°
• 1/cosec 230°

Note: Since 230° lies in the 3rd Quadrant, the final value of sin 230° will be negative.

We can use trigonometric identities to represent sin 230° as,

• sin(180° - 230°) = sin(-50°)
• -sin(180° + 230°) = -sin 410°
• cos(90° - 230°) = cos(-140°)
• -cos(90° + 230°) = -cos 320°

☛ Also Check:

• sin 150 degrees
• sin 15 degrees
• sin 50 degrees
• sin 31 degrees
• sin 1500 degrees
• sin 600 degrees

FAQs on Sin 230 Degrees

What is Sin 230 Degrees?

Sin 230 degrees is the value of sine trigonometric function for an angle equal to 230 degrees. The value of sin 230° is -0.766 (approx).

How to Find the Value of Sin 230 Degrees?

The value of sin 230 degrees can be calculated by constructing an angle of 230° with the x-axis, and then finding the coordinates of the corresponding point (-0.6428, -0.766) on the unit circle. The value of sin 230° is equal to the y-coordinate (-0.766). ∴ sin 230° = -0.766.

What is the Value of Sin 230 Degrees in Terms of Cos 230°?

Using trigonometric identities, we can write sin 230° in terms of cos 230° as, sin(230°) = -√(1-cos²(230°)). Here, the value of cos 230° is equal to -0.6427876.

What is the Value of Sin 230° in Terms of Cosec 230°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 230° as 1/cosec(230°). The value of cosec 230° is equal to -1.30540.

How to Find Sin 230° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 230° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(230°))
• ± tan 230°/√(1 + tan²(230°))
• ± 1/√(1 + cot²(230°))
• ± √(sec²(230°) - 1)/sec 230°
• 1/cosec 230°

☛ Also check: trigonometric table