Sin 255 Degrees

The value of sin 255 degrees is -0.9659258. . .. Sin 255 degrees in radians is written as sin (255° × π/180°), i.e., sin (17π/12) or sin (4.450589. . .). In this article, we will discuss the methods to find the value of sin 255 degrees with examples.

• Sin 255°: -0.9659258. . .
• Sin 255° in fraction: -(√6 + √2)/4
• Sin (-255 degrees): 0.9659258. . .
• Sin 255° in radians: sin (17π/12) or sin (4.4505895 . . .)

What is the Value of Sin 255 Degrees?

The value of sin 255 degrees in decimal is -0.965925826. . .. Sin 255 degrees can also be expressed using the equivalent of the given angle (255 degrees) in radians (4.45058 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 255 degrees = 255° × (π/180°) rad = 17π/12 or 4.4505 . . .
∴ sin 255° = sin(4.4505) = -(√6 + √2)/4 or -0.9659258. . .

Explanation:

For sin 255 degrees, the angle 255° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 255° value = -(√6 + √2)/4 or -0.9659258. . .
Since the sine function is a periodic function, we can represent sin 255° as, sin 255 degrees = sin(255° + n × 360°), n ∈ Z.
⇒ sin 255° = sin 615° = sin 975°, and so on.
Note: Since, sine is an odd function, the value of sin(-255°) = -sin(255°).

Methods to Find Value of Sin 255 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 255° is given as -0.96592. . .. We can find the value of sin 255 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 255° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 255 degrees as:

• ± √(1-cos²(255°))
• ± tan 255°/√(1 + tan²(255°))
• ± 1/√(1 + cot²(255°))
• ± √(sec²(255°) - 1)/sec 255°
• 1/cosec 255°

Note: Since 255° lies in the 3rd Quadrant, the final value of sin 255° will be negative.

We can use trigonometric identities to represent sin 255° as,

• sin(180° - 255°) = sin(-75°)
• -sin(180° + 255°) = -sin 435°
• cos(90° - 255°) = cos(-165°)
• -cos(90° + 255°) = -cos 345°

Sin 255 Degrees Using Unit Circle

To find the value of sin 255 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 255° angle with the positive x-axis.
• The sin of 255 degrees equals the y-coordinate(-0.9659) of the point of intersection (-0.2588, -0.9659) of unit circle and r.

Hence the value of sin 255° = y = -0.9659 (approx)

☛ Also Check:

• sin 120 degrees
• sin 556 degrees
• sin 18 degrees
• sin 66 degrees
• sin 390 degrees
• sin 24 degrees

FAQs on Sin 255 Degrees

What is Sin 255 Degrees?

Sin 255 degrees is the value of sine trigonometric function for an angle equal to 255 degrees. The value of sin 255° is -(√6 + √2)/4 or -0.9659 (approx).

How to Find the Value of Sin 255 Degrees?

The value of sin 255 degrees can be calculated by constructing an angle of 255° with the x-axis, and then finding the coordinates of the corresponding point (-0.2588, -0.9659) on the unit circle. The value of sin 255° is equal to the y-coordinate (-0.9659). ∴ sin 255° = -0.9659.

How to Find Sin 255° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 255° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(255°))
• ± tan 255°/√(1 + tan²(255°))
• ± 1/√(1 + cot²(255°))
• ± √(sec²(255°) - 1)/sec 255°
• 1/cosec 255°

☛ Also check: trigonometry table

What is the Value of Sin 255 Degrees in Terms of Tan 255°?

We know, using trig identities, we can write sin 255° as -tan 255°/√(1 + tan²(255°)). Here, the value of tan 255° is equal to 3.732050.

What is the Value of Sin 255° in Terms of Cosec 255°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 255° as 1/cosec(255°). The value of cosec 255° is equal to -1.03527.