Sin 129 Degrees

The value of sin 129 degrees is 0.7771459. . .. Sin 129 degrees in radians is written as sin (129° × π/180°), i.e., sin (43π/60) or sin (2.251474. . .). In this article, we will discuss the methods to find the value of sin 129 degrees with examples.

• Sin 129°: 0.7771459. . .
• Sin (-129 degrees): -0.7771459. . .
• Sin 129° in radians: sin (43π/60) or sin (2.2514747 . . .)

What is the Value of Sin 129 Degrees?

The value of sin 129 degrees in decimal is 0.777145961. . .. Sin 129 degrees can also be expressed using the equivalent of the given angle (129 degrees) in radians (2.25147 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 129 degrees = 129° × (π/180°) rad = 43π/60 or 2.2514 . . .
∴ sin 129° = sin(2.2514) = 0.7771459. . .

Explanation:

For sin 129 degrees, the angle 129° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 129° value = 0.7771459. . .
Since the sine function is a periodic function, we can represent sin 129° as, sin 129 degrees = sin(129° + n × 360°), n ∈ Z.
⇒ sin 129° = sin 489° = sin 849°, and so on.
Note: Since, sine is an odd function, the value of sin(-129°) = -sin(129°).

Methods to Find Value of Sin 129 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 129° is given as 0.77714. . .. We can find the value of sin 129 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 129 Degrees Using Unit Circle

To find the value of sin 129 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 129° angle with the positive x-axis.
• The sin of 129 degrees equals the y-coordinate(0.7771) of the point of intersection (-0.6293, 0.7771) of unit circle and r.

Hence the value of sin 129° = y = 0.7771 (approx)

Sin 129° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 129 degrees as:

• ± √(1-cos²(129°))
• ± tan 129°/√(1 + tan²(129°))
• ± 1/√(1 + cot²(129°))
• ± √(sec²(129°) - 1)/sec 129°
• 1/cosec 129°

Note: Since 129° lies in the 2nd Quadrant, the final value of sin 129° will be positive.

We can use trigonometric identities to represent sin 129° as,

• sin(180° - 129°) = sin 51°
• -sin(180° + 129°) = -sin 309°
• cos(90° - 129°) = cos(-39°)
• -cos(90° + 129°) = -cos 219°

☛ Also Check:

• sin 37 degrees
• sin 3 degrees
• sin 180 degrees
• sin 225 degrees
• sin 34 degrees
• sin 95 degrees

FAQs on Sin 129 Degrees

What is Sin 129 Degrees?

Sin 129 degrees is the value of sine trigonometric function for an angle equal to 129 degrees. The value of sin 129° is 0.7771 (approx).

How to Find Sin 129° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 129° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(129°))
• ± tan 129°/√(1 + tan²(129°))
• ± 1/√(1 + cot²(129°))
• ± √(sec²(129°) - 1)/sec 129°
• 1/cosec 129°

☛ Also check: trigonometry table

What is the Value of Sin 129° in Terms of Sec 129°?

Since the sine function can be represented using the secant function, we can write sin 129° as -√(sec²(129°) - 1)/sec 129°. The value of sec 129° is equal to -1.589016.

What is the Value of Sin 129 Degrees in Terms of Cos 129°?

Using trigonometric identities, we can write sin 129° in terms of cos 129° as, sin(129°) = √(1-cos²(129°)). Here, the value of cos 129° is equal to -0.6293203.

How to Find the Value of Sin 129 Degrees?

The value of sin 129 degrees can be calculated by constructing an angle of 129° with the x-axis, and then finding the coordinates of the corresponding point (-0.6293, 0.7771) on the unit circle. The value of sin 129° is equal to the y-coordinate (0.7771). ∴ sin 129° = 0.7771.