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:

• ± √(1-cos²(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 x-axis.
• The sin of 5 degrees equals the y-coordinate(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:

• sin 15 degrees
• sin 180 degrees
• sin 90 degrees
• sin 750 degrees
• sin 57 degrees
• sin 71 degrees

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:

• ± √(1-cos²(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 x-axis, 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 y-coordinate (0.0872). ∴ sin 5° = 0.0872.