Sin 115 Degrees

The value of sin 115 degrees is 0.9063077. . .. Sin 115 degrees in radians is written as sin (115° × π/180°), i.e., sin (23π/36) or sin (2.007128. . .). In this article, we will discuss the methods to find the value of sin 115 degrees with examples.

• Sin 115°: 0.9063077. . .
• Sin (-115 degrees): -0.9063077. . .
• Sin 115° in radians: sin (23π/36) or sin (2.0071286 . . .)

What is the Value of Sin 115 Degrees?

The value of sin 115 degrees in decimal is 0.906307787. . .. Sin 115 degrees can also be expressed using the equivalent of the given angle (115 degrees) in radians (2.00712 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 115 degrees = 115° × (π/180°) rad = 23π/36 or 2.0071 . . .
∴ sin 115° = sin(2.0071) = 0.9063077. . .

Explanation:

For sin 115 degrees, the angle 115° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 115° value = 0.9063077. . .
Since the sine function is a periodic function, we can represent sin 115° as, sin 115 degrees = sin(115° + n × 360°), n ∈ Z.
⇒ sin 115° = sin 475° = sin 835°, and so on.
Note: Since, sine is an odd function, the value of sin(-115°) = -sin(115°).

Methods to Find Value of Sin 115 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 115° is given as 0.90630. . .. We can find the value of sin 115 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 115 Degrees Using Unit Circle

To find the value of sin 115 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 115° angle with the positive x-axis.
• The sin of 115 degrees equals the y-coordinate(0.9063) of the point of intersection (-0.4226, 0.9063) of unit circle and r.

Hence the value of sin 115° = y = 0.9063 (approx)

Sin 115° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 115 degrees as:

• ± √(1-cos²(115°))
• ± tan 115°/√(1 + tan²(115°))
• ± 1/√(1 + cot²(115°))
• ± √(sec²(115°) - 1)/sec 115°
• 1/cosec 115°

Note: Since 115° lies in the 2nd Quadrant, the final value of sin 115° will be positive.

We can use trigonometric identities to represent sin 115° as,

• sin(180° - 115°) = sin 65°
• -sin(180° + 115°) = -sin 295°
• cos(90° - 115°) = cos(-25°)
• -cos(90° + 115°) = -cos 205°

☛ Also Check:

• sin 37 degrees
• sin 45 degrees
• sin 135 degrees
• sin 510 degrees
• sin 660 degrees
• sin 210 degrees

FAQs on Sin 115 Degrees

What is Sin 115 Degrees?

Sin 115 degrees is the value of sine trigonometric function for an angle equal to 115 degrees. The value of sin 115° is 0.9063 (approx).

How to Find Sin 115° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 115° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(115°))
• ± tan 115°/√(1 + tan²(115°))
• ± 1/√(1 + cot²(115°))
• ± √(sec²(115°) - 1)/sec 115°
• 1/cosec 115°

☛ Also check: trigonometry table

How to Find the Value of Sin 115 Degrees?

The value of sin 115 degrees can be calculated by constructing an angle of 115° with the x-axis, and then finding the coordinates of the corresponding point (-0.4226, 0.9063) on the unit circle. The value of sin 115° is equal to the y-coordinate (0.9063). ∴ sin 115° = 0.9063.

What is the Exact Value of sin 115 Degrees?

The exact value of sin 115 degrees can be given accurately up to 8 decimal places as 0.90630778.

What is the Value of Sin 115 Degrees in Terms of Tan 115°?

We know, using trig identities, we can write sin 115° as -tan 115°/√(1 + tan²(115°)). Here, the value of tan 115° is equal to -2.144506.