Sin 14 Degrees

The value of sin 14 degrees is 0.2419218. . .. Sin 14 degrees in radians is written as sin (14° × π/180°), i.e., sin (7π/90) or sin (0.244346. . .). In this article, we will discuss the methods to find the value of sin 14 degrees with examples.

• Sin 14°: 0.2419218. . .
• Sin (-14 degrees): -0.2419218. . .
• Sin 14° in radians: sin (7π/90) or sin (0.2443460 . . .)

What is the Value of Sin 14 Degrees?

The value of sin 14 degrees in decimal is 0.241921895. . .. Sin 14 degrees can also be expressed using the equivalent of the given angle (14 degrees) in radians (0.24434 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 14 degrees = 14° × (π/180°) rad = 7π/90 or 0.2443 . . .
∴ sin 14° = sin(0.2443) = 0.2419218. . .

Explanation:

For sin 14 degrees, the angle 14° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 14° value = 0.2419218. . .
Since the sine function is a periodic function, we can represent sin 14° as, sin 14 degrees = sin(14° + n × 360°), n ∈ Z.
⇒ sin 14° = sin 374° = sin 734°, and so on.
Note: Since, sine is an odd function, the value of sin(-14°) = -sin(14°).

Methods to Find Value of Sin 14 Degrees

The sine function is positive in the 1st quadrant. The value of sin 14° is given as 0.24192. . .. We can find the value of sin 14 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 14° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 14 degrees as:

• ± √(1-cos²(14°))
• ± tan 14°/√(1 + tan²(14°))
• ± 1/√(1 + cot²(14°))
• ± √(sec²(14°) - 1)/sec 14°
• 1/cosec 14°

Note: Since 14° lies in the 1st Quadrant, the final value of sin 14° will be positive.

We can use trigonometric identities to represent sin 14° as,

• sin(180° - 14°) = sin 166°
• -sin(180° + 14°) = -sin 194°
• cos(90° - 14°) = cos 76°
• -cos(90° + 14°) = -cos 104°

Sin 14 Degrees Using Unit Circle

To find the value of sin 14 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 14° angle with the positive x-axis.
• The sin of 14 degrees equals the y-coordinate(0.2419) of the point of intersection (0.9703, 0.2419) of unit circle and r.

Hence the value of sin 14° = y = 0.2419 (approx)

☛ Also Check:

• sin 40 degrees
• sin 90 degrees
• sin 0 degrees
• sin 656 degrees
• sin 42 degrees
• sin 585 degrees

FAQs on Sin 14 Degrees

What is Sin 14 Degrees?

Sin 14 degrees is the value of sine trigonometric function for an angle equal to 14 degrees. The value of sin 14° is 0.2419 (approx).

How to Find Sin 14° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 14° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(14°))
• ± tan 14°/√(1 + tan²(14°))
• ± 1/√(1 + cot²(14°))
• ± √(sec²(14°) - 1)/sec 14°
• 1/cosec 14°

☛ Also check: trigonometry table

What is the Value of Sin 14 Degrees in Terms of Cos 14°?

Using trigonometric identities, we can write sin 14° in terms of cos 14° as, sin(14°) = √(1-cos²(14°)). Here, the value of cos 14° is equal to 0.9702957.

What is the Value of Sin 14° in Terms of Sec 14°?

Since the sine function can be represented using the secant function, we can write sin 14° as √(sec²(14°) - 1)/sec 14°. The value of sec 14° is equal to 1.030614.

How to Find the Value of Sin 14 Degrees?

The value of sin 14 degrees can be calculated by constructing an angle of 14° with the x-axis, and then finding the coordinates of the corresponding point (0.9703, 0.2419) on the unit circle. The value of sin 14° is equal to the y-coordinate (0.2419). ∴ sin 14° = 0.2419.