Sin 10 Degrees

The value of sin 10 degrees is 0.1736481. . .. Sin 10 degrees in radians is written as sin (10° × π/180°), i.e., sin (π/18) or sin (0.174532. . .). In this article, we will discuss the methods to find the value of sin 10 degrees with examples.

• Sin 10°: 0.1736481. . .
• Sin (-10 degrees): -0.1736481. . .
• Sin 10° in radians: sin (π/18) or sin (0.1745329 . . .)

What is the Value of Sin 10 Degrees?

The value of sin 10 degrees in decimal is 0.173648177. . .. Sin 10 degrees can also be expressed using the equivalent of the given angle (10 degrees) in radians (0.17453 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 10 degrees = 10° × (π/180°) rad = π/18 or 0.1745 . . .
∴ sin 10° = sin(0.1745) = 0.1736481. . .

Explanation:

For sin 10 degrees, the angle 10° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 10° value = 0.1736481. . .
Since the sine function is a periodic function, we can represent sin 10° as, sin 10 degrees = sin(10° + n × 360°), n ∈ Z.
⇒ sin 10° = sin 370° = sin 730°, and so on.
Note: Since, sine is an odd function, the value of sin(-10°) = -sin(10°).

Methods to Find Value of Sin 10 Degrees

The sine function is positive in the 1st quadrant. The value of sin 10° is given as 0.17364. . .. We can find the value of sin 10 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 10° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 10 degrees as:

• ± √(1-cos²(10°))
• ± tan 10°/√(1 + tan²(10°))
• ± 1/√(1 + cot²(10°))
• ± √(sec²(10°) - 1)/sec 10°
• 1/cosec 10°

Note: Since 10° lies in the 1st Quadrant, the final value of sin 10° will be positive.

We can use trigonometric identities to represent sin 10° as,

• sin(180° - 10°) = sin 170°
• -sin(180° + 10°) = -sin 190°
• cos(90° - 10°) = cos 80°
• -cos(90° + 10°) = -cos 100°

Sin 10 Degrees Using Unit Circle

To find the value of sin 10 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 10° angle with the positive x-axis.
• The sin of 10 degrees equals the y-coordinate(0.1736) of the point of intersection (0.9848, 0.1736) of unit circle and r.

Hence the value of sin 10° = y = 0.1736 (approx)

☛ Also Check:

• sin 135 degrees
• sin 37 degrees
• sin 11 degrees
• sin 29 degrees
• sin 910 degrees
• sin 19 degrees

FAQs on Sin 10 Degrees

What is Sin 10 Degrees?

Sin 10 degrees is the value of sine trigonometric function for an angle equal to 10 degrees. The value of sin 10° is 0.1736 (approx).

What is the Value of Sin 10 Degrees in Terms of Cos 10°?

Using trigonometric identities, we can write sin 10° in terms of cos 10° as, sin(10°) = √(1-cos²(10°)). Here, the value of cos 10° is equal to 0.9848077.

What is the Value of Sin 10° in Terms of Sec 10°?

Since the sine function can be represented using the secant function, we can write sin 10° as √(sec²(10°) - 1)/sec 10°. The value of sec 10° is equal to 1.015427.

How to Find the Value of Sin 10 Degrees?

The value of sin 10 degrees can be calculated by constructing an angle of 10° with the x-axis, and then finding the coordinates of the corresponding point (0.9848, 0.1736) on the unit circle. The value of sin 10° is equal to the y-coordinate (0.1736). ∴ sin 10° = 0.1736.

How to Find Sin 10° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 10° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(10°))
• ± tan 10°/√(1 + tan²(10°))
• ± 1/√(1 + cot²(10°))
• ± √(sec²(10°) - 1)/sec 10°
• 1/cosec 10°

☛ Also check: trigonometry table