Sin 5 Degrees
The value of sin 5 degrees is 0.0871557. . .. Sin 5 degrees in radians is written as sin (5° × π/180°), i.e., sin (π/36) or sin (0.087266. . .). In this article, we will discuss the methods to find the value of sin 5 degrees with examples.
 Sin 5°: 0.0871557. . .
 Sin (5 degrees): 0.0871557. . .
 Sin 5° in radians: sin (π/36) or sin (0.0872664 . . .)
What is the Value of Sin 5 Degrees?
The value of sin 5 degrees in decimal is 0.087155742. . .. Sin 5 degrees can also be expressed using the equivalent of the given angle (5 degrees) in radians (0.08726 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 5 degrees = 5° × (π/180°) rad = π/36 or 0.0872 . . .
∴ sin 5° = sin(0.0872) = 0.0871557. . .
Explanation:
For sin 5 degrees, the angle 5° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 5° value = 0.0871557. . .
Since the sine function is a periodic function, we can represent sin 5° as, sin 5 degrees = sin(5° + n × 360°), n ∈ Z.
⇒ sin 5° = sin 365° = sin 725°, and so on.
Note: Since, sine is an odd function, the value of sin(5°) = sin(5°).
Methods to Find Value of Sin 5 Degrees
The sine function is positive in the 1st quadrant. The value of sin 5° is given as 0.08715. . .. We can find the value of sin 5 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 5° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 5 degrees as:
 ± √(1cos²(5°))
 ± tan 5°/√(1 + tan²(5°))
 ± 1/√(1 + cot²(5°))
 ± √(sec²(5°)  1)/sec 5°
 1/cosec 5°
Note: Since 5° lies in the 1st Quadrant, the final value of sin 5° will be positive.
We can use trigonometric identities to represent sin 5° as,
 sin(180°  5°) = sin 175°
 sin(180° + 5°) = sin 185°
 cos(90°  5°) = cos 85°
 cos(90° + 5°) = cos 95°
Sin 5 Degrees Using Unit Circle
To find the value of sin 5 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form a 5° angle with the positive xaxis.
 The sin of 5 degrees equals the ycoordinate(0.0872) of the point of intersection (0.9962, 0.0872) of unit circle and r.
Hence the value of sin 5° = y = 0.0872 (approx)
☛ Also Check:
Examples Using Sin 5 Degrees

Example 1: Simplify: 2 (sin 5°/sin 365°)
Solution:
We know sin 5° = sin 365°
⇒ 2 sin 5°/sin 365° = 2(sin 5°/sin 5°)
= 2(1) = 2 
Example 2: Find the value of 2 × (sin 2.5° cos 2.5°). [Hint: Use sin 5° = 0.0872]
Solution:
Using the sin 2a formula,
2 sin 2.5° cos 2.5° = sin(2 × 2.5°) = sin 5°
∵ sin 5° = 0.0872
⇒ 2 × (sin 2.5° cos 2.5°) = 0.0872 
Example 3: Find the value of 5 sin(5°)/7 cos(85°).
Solution:
Using trigonometric identities, we know, sin(5°) = cos(90°  5°) = cos 85°.
⇒ sin(5°) = cos(85°)
⇒ Value of 5 sin(5°)/7 cos(85°) = 5/7
FAQs on Sin 5 Degrees
What is Sin 5 Degrees?
Sin 5 degrees is the value of sine trigonometric function for an angle equal to 5 degrees. The value of sin 5° is 0.0872 (approx).
How to Find Sin 5° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 5° can be given in terms of other trigonometric functions as:
 ± √(1cos²(5°))
 ± tan 5°/√(1 + tan²(5°))
 ± 1/√(1 + cot²(5°))
 ± √(sec²(5°)  1)/sec 5°
 1/cosec 5°
☛ Also check: trigonometric table
What is the Exact Value of sin 5 Degrees?
The exact value of sin 5 degrees can be given accurately up to 8 decimal places as 0.08715574.
What is the Value of Sin 5 Degrees in Terms of Tan 5°?
We know, using trig identities, we can write sin 5° as tan 5°/√(1 + tan²(5°)). Here, the value of tan 5° is equal to 0.087488.
How to Find the Value of Sin 5 Degrees?
The value of sin 5 degrees can be calculated by constructing an angle of 5° with the xaxis, and then finding the coordinates of the corresponding point (0.9962, 0.0872) on the unit circle. The value of sin 5° is equal to the ycoordinate (0.0872). ∴ sin 5° = 0.0872.
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