Sin 130 Degrees

The value of sin 130 degrees is 0.7660444. . .. Sin 130 degrees in radians is written as sin (130° × π/180°), i.e., sin (13π/18) or sin (2.268928. . .). In this article, we will discuss the methods to find the value of sin 130 degrees with examples.

• Sin 130°: 0.7660444. . .
• Sin (-130 degrees): -0.7660444. . .
• Sin 130° in radians: sin (13π/18) or sin (2.2689280 . . .)

What is the Value of Sin 130 Degrees?

The value of sin 130 degrees in decimal is 0.766044443. . .. Sin 130 degrees can also be expressed using the equivalent of the given angle (130 degrees) in radians (2.26892 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 130 degrees = 130° × (π/180°) rad = 13π/18 or 2.2689 . . .
∴ sin 130° = sin(2.2689) = 0.7660444. . .

Explanation:

For sin 130 degrees, the angle 130° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 130° value = 0.7660444. . .
Since the sine function is a periodic function, we can represent sin 130° as, sin 130 degrees = sin(130° + n × 360°), n ∈ Z.
⇒ sin 130° = sin 490° = sin 850°, and so on.
Note: Since, sine is an odd function, the value of sin(-130°) = -sin(130°).

Methods to Find Value of Sin 130 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 130° is given as 0.76604. . .. We can find the value of sin 130 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 130 Degrees Using Unit Circle

To find the value of sin 130 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 130° angle with the positive x-axis.
• The sin of 130 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 130° = y = 0.766 (approx)

Sin 130° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 130 degrees as:

• ± √(1-cos²(130°))
• ± tan 130°/√(1 + tan²(130°))
• ± 1/√(1 + cot²(130°))
• ± √(sec²(130°) - 1)/sec 130°
• 1/cosec 130°

Note: Since 130° lies in the 2nd Quadrant, the final value of sin 130° will be positive.

We can use trigonometric identities to represent sin 130° as,

• sin(180° - 130°) = sin 50°
• -sin(180° + 130°) = -sin 310°
• cos(90° - 130°) = cos(-40°)
• -cos(90° + 130°) = -cos 220°

☛ Also Check:

• sin 18 degrees
• sin 60 degrees
• sin 90 degrees
• sin 230 degrees
• sin 12 degrees
• sin 83 degrees

FAQs on Sin 130 Degrees

What is Sin 130 Degrees?

Sin 130 degrees is the value of sine trigonometric function for an angle equal to 130 degrees. The value of sin 130° is 0.766 (approx).

What is the Value of Sin 130° in Terms of Cosec 130°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 130° as 1/cosec(130°). The value of cosec 130° is equal to 1.30540.

What is the Value of Sin 130 Degrees in Terms of Tan 130°?

We know, using trig identities, we can write sin 130° as -tan 130°/√(1 + tan²(130°)). Here, the value of tan 130° is equal to -1.191753.

How to Find Sin 130° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 130° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(130°))
• ± tan 130°/√(1 + tan²(130°))
• ± 1/√(1 + cot²(130°))
• ± √(sec²(130°) - 1)/sec 130°
• 1/cosec 130°

☛ Also check: trigonometry table

How to Find the Value of Sin 130 Degrees?

The value of sin 130 degrees can be calculated by constructing an angle of 130° 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 130° is equal to the y-coordinate (0.766). ∴ sin 130° = 0.766.