Sin 127 Degrees

The value of sin 127 degrees is 0.7986355. . .. Sin 127 degrees in radians is written as sin (127° × π/180°), i.e., sin (2.216568. . .). In this article, we will discuss the methods to find the value of sin 127 degrees with examples.

• Sin 127°: 0.7986355. . .
• Sin (-127 degrees): -0.7986355. . .
• Sin 127° in radians: sin (2.2165681 . . .)

What is the Value of Sin 127 Degrees?

The value of sin 127 degrees in decimal is 0.798635510. . .. Sin 127 degrees can also be expressed using the equivalent of the given angle (127 degrees) in radians (2.21656 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 127 degrees = 127° × (π/180°) rad = 2.2165 . . .
∴ sin 127° = sin(2.2165) = 0.7986355. . .

Explanation:

For sin 127 degrees, the angle 127° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 127° value = 0.7986355. . .
Since the sine function is a periodic function, we can represent sin 127° as, sin 127 degrees = sin(127° + n × 360°), n ∈ Z.
⇒ sin 127° = sin 487° = sin 847°, and so on.
Note: Since, sine is an odd function, the value of sin(-127°) = -sin(127°).

Methods to Find Value of Sin 127 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 127° is given as 0.79863. . .. We can find the value of sin 127 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 127 Degrees Using Unit Circle

To find the value of sin 127 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 127° angle with the positive x-axis.
• The sin of 127 degrees equals the y-coordinate(0.7986) of the point of intersection (-0.6018, 0.7986) of unit circle and r.

Hence the value of sin 127° = y = 0.7986 (approx)

Sin 127° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 127 degrees as:

• ± √(1-cos²(127°))
• ± tan 127°/√(1 + tan²(127°))
• ± 1/√(1 + cot²(127°))
• ± √(sec²(127°) - 1)/sec 127°
• 1/cosec 127°

Note: Since 127° lies in the 2nd Quadrant, the final value of sin 127° will be positive.

We can use trigonometric identities to represent sin 127° as,

• sin(180° - 127°) = sin 53°
• -sin(180° + 127°) = -sin 307°
• cos(90° - 127°) = cos(-37°)
• -cos(90° + 127°) = -cos 217°

☛ Also Check:

• sin 53 degrees
• sin 40 degrees
• sin 30 degrees
• sin 28 degrees
• sin 206 degrees
• sin 25 degrees

FAQs on Sin 127 Degrees

What is Sin 127 Degrees?

Sin 127 degrees is the value of sine trigonometric function for an angle equal to 127 degrees. The value of sin 127° is 0.7986 (approx).

What is the Value of Sin 127° in Terms of Sec 127°?

Since the sine function can be represented using the secant function, we can write sin 127° as -√(sec²(127°) - 1)/sec 127°. The value of sec 127° is equal to -1.66164.

How to Find the Value of Sin 127 Degrees?

The value of sin 127 degrees can be calculated by constructing an angle of 127° with the x-axis, and then finding the coordinates of the corresponding point (-0.6018, 0.7986) on the unit circle. The value of sin 127° is equal to the y-coordinate (0.7986). ∴ sin 127° = 0.7986.

How to Find Sin 127° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 127° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(127°))
• ± tan 127°/√(1 + tan²(127°))
• ± 1/√(1 + cot²(127°))
• ± √(sec²(127°) - 1)/sec 127°
• 1/cosec 127°

☛ Also check: trigonometric table

What is the Value of Sin 127 Degrees in Terms of Tan 127°?

We know, using trig identities, we can write sin 127° as -tan 127°/√(1 + tan²(127°)). Here, the value of tan 127° is equal to -1.327044.