Sin 108 Degrees

The value of sin 108 degrees is 0.9510565. . .. Sin 108 degrees in radians is written as sin (108° × π/180°), i.e., sin (3π/5) or sin (1.884955. . .). In this article, we will discuss the methods to find the value of sin 108 degrees with examples.

• Sin 108°: 0.9510565. . .
• Sin (-108 degrees): -0.9510565. . .
• Sin 108° in radians: sin (3π/5) or sin (1.8849555 . . .)

What is the Value of Sin 108 Degrees?

The value of sin 108 degrees in decimal is 0.951056516. . .. Sin 108 degrees can also be expressed using the equivalent of the given angle (108 degrees) in radians (1.88495 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 108 degrees = 108° × (π/180°) rad = 3π/5 or 1.8849 . . .
∴ sin 108° = sin(1.8849) = 0.9510565. . .

Explanation:

For sin 108 degrees, the angle 108° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 108° value = 0.9510565. . .
Since the sine function is a periodic function, we can represent sin 108° as, sin 108 degrees = sin(108° + n × 360°), n ∈ Z.
⇒ sin 108° = sin 468° = sin 828°, and so on.
Note: Since, sine is an odd function, the value of sin(-108°) = -sin(108°).

Methods to Find Value of Sin 108 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 108° is given as 0.95105. . .. We can find the value of sin 108 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 108° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 108 degrees as:

• ± √(1-cos²(108°))
• ± tan 108°/√(1 + tan²(108°))
• ± 1/√(1 + cot²(108°))
• ± √(sec²(108°) - 1)/sec 108°
• 1/cosec 108°

Note: Since 108° lies in the 2nd Quadrant, the final value of sin 108° will be positive.

We can use trigonometric identities to represent sin 108° as,

• sin(180° - 108°) = sin 72°
• -sin(180° + 108°) = -sin 288°
• cos(90° - 108°) = cos(-18°)
• -cos(90° + 108°) = -cos 198°

Sin 108 Degrees Using Unit Circle

To find the value of sin 108 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 108° angle with the positive x-axis.
• The sin of 108 degrees equals the y-coordinate(0.9511) of the point of intersection (-0.309, 0.9511) of unit circle and r.

Hence the value of sin 108° = y = 0.9511 (approx)

☛ Also Check:

• sin 556 degrees
• sin 11 degrees
• sin 270 degrees
• sin 83 degrees
• sin 690 degrees
• sin 43 degrees

FAQs on Sin 108 Degrees

What is Sin 108 Degrees?

Sin 108 degrees is the value of sine trigonometric function for an angle equal to 108 degrees. The value of sin 108° is 0.9511 (approx).

How to Find Sin 108° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 108° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(108°))
• ± tan 108°/√(1 + tan²(108°))
• ± 1/√(1 + cot²(108°))
• ± √(sec²(108°) - 1)/sec 108°
• 1/cosec 108°

☛ Also check: trigonometric table

What is the Value of Sin 108 Degrees in Terms of Tan 108°?

We know, using trig identities, we can write sin 108° as -tan 108°/√(1 + tan²(108°)). Here, the value of tan 108° is equal to -3.077683.

What is the Value of Sin 108° in Terms of Cosec 108°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 108° as 1/cosec(108°). The value of cosec 108° is equal to 1.05146.

How to Find the Value of Sin 108 Degrees?

The value of sin 108 degrees can be calculated by constructing an angle of 108° with the x-axis, and then finding the coordinates of the corresponding point (-0.309, 0.9511) on the unit circle. The value of sin 108° is equal to the y-coordinate (0.9511). ∴ sin 108° = 0.9511.