Sin 18 Degrees

The value of sin 18 degrees is 0.3090169. . .. Sin 18 degrees in radians is written as sin (18° × π/180°), i.e., sin (π/10) or sin (0.314159. . .). In this article, we will discuss the methods to find the value of sin 18 degrees with examples.

• Sin 18°: 0.3090169. . .
• Sin 18° in fraction: (√5 - 1)/4
• Sin (-18 degrees): -0.3090169. . .
• Sin 18° in radians: sin (π/10) or sin (0.3141592 . . .)

What is the Value of Sin 18 Degrees?

The value of sin 18 degrees in decimal is 0.309016994. . .. Sin 18 degrees can also be expressed using the equivalent of the given angle (18 degrees) in radians (0.31415 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 18 degrees = 18° × (π/180°) rad = π/10 or 0.3141 . . .
∴ sin 18° = sin(0.3141) = (√5 - 1)/4 or 0.3090169. . .

Explanation:

For sin 18 degrees, the angle 18° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 18° value = (√5 - 1)/4 or 0.3090169. . .
Since the sine function is a periodic function, we can represent sin 18° as, sin 18 degrees = sin(18° + n × 360°), n ∈ Z.
⇒ sin 18° = sin 378° = sin 738°, and so on.
Note: Since, sine is an odd function, the value of sin(-18°) = -sin(18°).

Methods to Find Value of Sin 18 Degrees

The sine function is positive in the 1st quadrant. The value of sin 18° is given as 0.30901. . .. We can find the value of sin 18 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 18° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 18 degrees as:

• ± √(1-cos²(18°))
• ± tan 18°/√(1 + tan²(18°))
• ± 1/√(1 + cot²(18°))
• ± √(sec²(18°) - 1)/sec 18°
• 1/cosec 18°

Note: Since 18° lies in the 1st Quadrant, the final value of sin 18° will be positive.

We can use trigonometric identities to represent sin 18° as,

• sin(180° - 18°) = sin 162°
• -sin(180° + 18°) = -sin 198°
• cos(90° - 18°) = cos 72°
• -cos(90° + 18°) = -cos 108°

Sin 18 Degrees Using Unit Circle

To find the value of sin 18 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 18° angle with the positive x-axis.
• The sin of 18 degrees equals the y-coordinate(0.309) of the point of intersection (0.9511, 0.309) of unit circle and r.

Hence the value of sin 18° = y = 0.309 (approx)

☛ Also Check:

• sin 75 degrees
• sin 50 degrees
• sin 30 degrees
• sin 16 degrees
• sin 260 degrees
• sin 73 degrees

FAQs on Sin 18 Degrees

What is Sin 18 Degrees?

Sin 18 degrees is the value of sine trigonometric function for an angle equal to 18 degrees. The value of sin 18° is (√5 - 1)/4 or 0.309 (approx).

How to Find Sin 18° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 18° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(18°))
• ± tan 18°/√(1 + tan²(18°))
• ± 1/√(1 + cot²(18°))
• ± √(sec²(18°) - 1)/sec 18°
• 1/cosec 18°

☛ Also check: trigonometry table

What is the Exact Value of sin 18 Degrees?

The exact value of sin 18 degrees can be given accurately up to 8 decimal places as 0.30901699 and (√5 - 1)/4 in fraction.

How to Find the Value of Sin 18 Degrees?

The value of sin 18 degrees can be calculated by constructing an angle of 18° with the x-axis, and then finding the coordinates of the corresponding point (0.9511, 0.309) on the unit circle. The value of sin 18° is equal to the y-coordinate (0.309). ∴ sin 18° = 0.309.

What is the Value of Sin 18 Degrees in Terms of Tan 18°?

We know, using trig identities, we can write sin 18° as tan 18°/√(1 + tan²(18°)). Here, the value of tan 18° is equal to 0.324919.