Sin 125 Degrees

The value of sin 125 degrees is 0.8191520. . .. Sin 125 degrees in radians is written as sin (125° × π/180°), i.e., sin (25π/36) or sin (2.181661. . .). In this article, we will discuss the methods to find the value of sin 125 degrees with examples.

• Sin 125°: 0.8191520. . .
• Sin (-125 degrees): -0.8191520. . .
• Sin 125° in radians: sin (25π/36) or sin (2.1816615 . . .)

What is the Value of Sin 125 Degrees?

The value of sin 125 degrees in decimal is 0.819152044. . .. Sin 125 degrees can also be expressed using the equivalent of the given angle (125 degrees) in radians (2.18166 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 125 degrees = 125° × (π/180°) rad = 25π/36 or 2.1816 . . .
∴ sin 125° = sin(2.1816) = 0.8191520. . .

Explanation:

For sin 125 degrees, the angle 125° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 125° value = 0.8191520. . .
Since the sine function is a periodic function, we can represent sin 125° as, sin 125 degrees = sin(125° + n × 360°), n ∈ Z.
⇒ sin 125° = sin 485° = sin 845°, and so on.
Note: Since, sine is an odd function, the value of sin(-125°) = -sin(125°).

Methods to Find Value of Sin 125 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 125° is given as 0.81915. . .. We can find the value of sin 125 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 125 Degrees Using Unit Circle

To find the value of sin 125 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 125° angle with the positive x-axis.
• The sin of 125 degrees equals the y-coordinate(0.8192) of the point of intersection (-0.5736, 0.8192) of unit circle and r.

Hence the value of sin 125° = y = 0.8192 (approx)

Sin 125° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 125 degrees as:

• ± √(1-cos²(125°))
• ± tan 125°/√(1 + tan²(125°))
• ± 1/√(1 + cot²(125°))
• ± √(sec²(125°) - 1)/sec 125°
• 1/cosec 125°

Note: Since 125° lies in the 2nd Quadrant, the final value of sin 125° will be positive.

We can use trigonometric identities to represent sin 125° as,

• sin(180° - 125°) = sin 55°
• -sin(180° + 125°) = -sin 305°
• cos(90° - 125°) = cos(-35°)
• -cos(90° + 125°) = -cos 215°

☛ Also Check:

• sin 36 degrees
• sin 270 degrees
• sin 30 degrees
• sin 49 degrees
• sin 41 degrees
• sin 495 degrees

FAQs on Sin 125 Degrees

What is Sin 125 Degrees?

Sin 125 degrees is the value of sine trigonometric function for an angle equal to 125 degrees. The value of sin 125° is 0.8192 (approx).

How to Find Sin 125° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 125° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(125°))
• ± tan 125°/√(1 + tan²(125°))
• ± 1/√(1 + cot²(125°))
• ± √(sec²(125°) - 1)/sec 125°
• 1/cosec 125°

☛ Also check: trigonometry table

How to Find the Value of Sin 125 Degrees?

The value of sin 125 degrees can be calculated by constructing an angle of 125° with the x-axis, and then finding the coordinates of the corresponding point (-0.5736, 0.8192) on the unit circle. The value of sin 125° is equal to the y-coordinate (0.8192). ∴ sin 125° = 0.8192.

What is the Value of Sin 125 Degrees in Terms of Cot 125°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 125° can be written as 1/√(1 + cot²(125°)). Here, the value of cot 125° is equal to -0.70020.

What is the Value of Sin 125° in Terms of Sec 125°?

Since the sine function can be represented using the secant function, we can write sin 125° as -√(sec²(125°) - 1)/sec 125°. The value of sec 125° is equal to -1.743447.