Sin 16 Degrees

The value of sin 16 degrees is 0.2756373. . .. Sin 16 degrees in radians is written as sin (16° × π/180°), i.e., sin (4π/45) or sin (0.279252. . .). In this article, we will discuss the methods to find the value of sin 16 degrees with examples.

• Sin 16°: 0.2756373. . .
• Sin (-16 degrees): -0.2756373. . .
• Sin 16° in radians: sin (4π/45) or sin (0.2792526 . . .)

What is the Value of Sin 16 Degrees?

The value of sin 16 degrees in decimal is 0.275637355. . .. Sin 16 degrees can also be expressed using the equivalent of the given angle (16 degrees) in radians (0.27925 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 16 degrees = 16° × (π/180°) rad = 4π/45 or 0.2792 . . .
∴ sin 16° = sin(0.2792) = 0.2756373. . .

Explanation:

For sin 16 degrees, the angle 16° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 16° value = 0.2756373. . .
Since the sine function is a periodic function, we can represent sin 16° as, sin 16 degrees = sin(16° + n × 360°), n ∈ Z.
⇒ sin 16° = sin 376° = sin 736°, and so on.
Note: Since, sine is an odd function, the value of sin(-16°) = -sin(16°).

Methods to Find Value of Sin 16 Degrees

The sine function is positive in the 1st quadrant. The value of sin 16° is given as 0.27563. . .. We can find the value of sin 16 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 16 Degrees Using Unit Circle

To find the value of sin 16 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 16° angle with the positive x-axis.
• The sin of 16 degrees equals the y-coordinate(0.2756) of the point of intersection (0.9613, 0.2756) of unit circle and r.

Hence the value of sin 16° = y = 0.2756 (approx)

Sin 16° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 16 degrees as:

• ± √(1-cos²(16°))
• ± tan 16°/√(1 + tan²(16°))
• ± 1/√(1 + cot²(16°))
• ± √(sec²(16°) - 1)/sec 16°
• 1/cosec 16°

Note: Since 16° lies in the 1st Quadrant, the final value of sin 16° will be positive.

We can use trigonometric identities to represent sin 16° as,

• sin(180° - 16°) = sin 164°
• -sin(180° + 16°) = -sin 196°
• cos(90° - 16°) = cos 74°
• -cos(90° + 16°) = -cos 106°

☛ Also Check:

• sin 60 degrees
• sin 30 degrees
• sin 120 degrees
• sin 19 degrees
• sin 1125 degrees
• sin 127 degrees

FAQs on Sin 16 Degrees

What is Sin 16 Degrees?

Sin 16 degrees is the value of sine trigonometric function for an angle equal to 16 degrees. The value of sin 16° is 0.2756 (approx).

What is the Value of Sin 16 Degrees in Terms of Cot 16°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 16° can be written as 1/√(1 + cot²(16°)). Here, the value of cot 16° is equal to 3.48741.

How to Find Sin 16° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 16° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(16°))
• ± tan 16°/√(1 + tan²(16°))
• ± 1/√(1 + cot²(16°))
• ± √(sec²(16°) - 1)/sec 16°
• 1/cosec 16°

☛ Also check: trigonometry table

How to Find the Value of Sin 16 Degrees?

The value of sin 16 degrees can be calculated by constructing an angle of 16° with the x-axis, and then finding the coordinates of the corresponding point (0.9613, 0.2756) on the unit circle. The value of sin 16° is equal to the y-coordinate (0.2756). ∴ sin 16° = 0.2756.

What is the Value of Sin 16° in Terms of Sec 16°?

Since the sine function can be represented using the secant function, we can write sin 16° as √(sec²(16°) - 1)/sec 16°. The value of sec 16° is equal to 1.040299.