Sin 36 Degrees

The value of sin 36 degrees is 0.5877852. . .. Sin 36 degrees in radians is written as sin (36° × π/180°), i.e., sin (π/5) or sin (0.628318. . .). In this article, we will discuss the methods to find the value of sin 36 degrees with examples.

• Sin 36°: 0.5877852. . .
• Sin 36° in fraction: √(10 - 2√5)/4
• Sin (-36 degrees): -0.5877852. . .
• Sin 36° in radians: sin (π/5) or sin (0.6283185 . . .)

What is the Value of Sin 36 Degrees?

The value of sin 36 degrees in decimal is 0.587785252. . .. Sin 36 degrees can also be expressed using the equivalent of the given angle (36 degrees) in radians (0.62831 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 36 degrees = 36° × (π/180°) rad = π/5 or 0.6283 . . .
∴ sin 36° = sin(0.6283) = √(10 - 2√5)/4 or 0.5877852. . .

Explanation:

For sin 36 degrees, the angle 36° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 36° value = √(10 - 2√5)/4 or 0.5877852. . .
Since the sine function is a periodic function, we can represent sin 36° as, sin 36 degrees = sin(36° + n × 360°), n ∈ Z.
⇒ sin 36° = sin 396° = sin 756°, and so on.
Note: Since, sine is an odd function, the value of sin(-36°) = -sin(36°).

Methods to Find Value of Sin 36 Degrees

The sine function is positive in the 1st quadrant. The value of sin 36° is given as 0.58778. . .. We can find the value of sin 36 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 36° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 36 degrees as:

• ± √(1-cos²(36°))
• ± tan 36°/√(1 + tan²(36°))
• ± 1/√(1 + cot²(36°))
• ± √(sec²(36°) - 1)/sec 36°
• 1/cosec 36°

Note: Since 36° lies in the 1st Quadrant, the final value of sin 36° will be positive.

We can use trigonometric identities to represent sin 36° as,

• sin(180° - 36°) = sin 144°
• -sin(180° + 36°) = -sin 216°
• cos(90° - 36°) = cos 54°
• -cos(90° + 36°) = -cos 126°

Sin 36 Degrees Using Unit Circle

To find the value of sin 36 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 36° angle with the positive x-axis.
• The sin of 36 degrees equals the y-coordinate(0.5878) of the point of intersection (0.809, 0.5878) of unit circle and r.

Hence the value of sin 36° = y = 0.5878 (approx)

☛ Also Check:

• sin 10 degrees
• sin 120 degrees
• sin 150 degrees
• sin 73 degrees
• sin 165 degrees
• sin 200 degrees

FAQs on Sin 36 Degrees

What is Sin 36 Degrees?

Sin 36 degrees is the value of sine trigonometric function for an angle equal to 36 degrees. The value of sin 36° is √(10 - 2√5)/4 or 0.5878 (approx).

What is the Value of Sin 36 Degrees in Terms of Tan 36°?

We know, using trig identities, we can write sin 36° as tan 36°/√(1 + tan²(36°)). Here, the value of tan 36° is equal to 0.726542.

What is the Value of Sin 36° in Terms of Sec 36°?

Since the sine function can be represented using the secant function, we can write sin 36° as √(sec²(36°) - 1)/sec 36°. The value of sec 36° is equal to 1.236068.

How to Find the Value of Sin 36 Degrees?

The value of sin 36 degrees can be calculated by constructing an angle of 36° with the x-axis, and then finding the coordinates of the corresponding point (0.809, 0.5878) on the unit circle. The value of sin 36° is equal to the y-coordinate (0.5878). ∴ sin 36° = 0.5878.

How to Find Sin 36° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 36° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(36°))
• ± tan 36°/√(1 + tan²(36°))
• ± 1/√(1 + cot²(36°))
• ± √(sec²(36°) - 1)/sec 36°
• 1/cosec 36°

☛ Also check: trigonometry table