Cos 16 Degrees

The value of cos 16 degrees is 0.9612616. . .. Cos 16 degrees in radians is written as cos (16° × π/180°), i.e., cos (4π/45) or cos (0.279252. . .). In this article, we will discuss the methods to find the value of cos 16 degrees with examples.

• Cos 16°: 0.9612616. . .
• Cos (-16 degrees): 0.9612616. . .
• Cos 16° in radians: cos (4π/45) or cos (0.2792526 . . .)

What is the Value of Cos 16 Degrees?

The value of cos 16 degrees in decimal is 0.961261695. . .. Cos 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 . . .
∴ cos 16° = cos(0.2792) = 0.9612616. . .

Explanation:

For cos 16 degrees, the angle 16° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 16° value = 0.9612616. . .
Since the cosine function is a periodic function, we can represent cos 16° as, cos 16 degrees = cos(16° + n × 360°), n ∈ Z.
⇒ cos 16° = cos 376° = cos 736°, and so on.
Note: Since, cosine is an even function, the value of cos(-16°) = cos(16°).

Methods to Find Value of Cos 16 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 16° is given as 0.96126. . .. We can find the value of cos 16 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 16 Degrees Using Unit Circle

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

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

Hence the value of cos 16° = x = 0.9613 (approx)

Cos 16° in Terms of Trigonometric Functions

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

• ± √(1-sin²(16°))
• ± 1/√(1 + tan²(16°))
• ± cot 16°/√(1 + cot²(16°))
• ±√(cosec²(16°) - 1)/cosec 16°
• 1/sec 16°

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

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

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

☛ Also Check:

• cos 53 degrees
• cos 90 degrees
• cos 37 degrees
• cos 95 degrees
• cos 41 degrees
• cos 326 degrees

FAQs on Cos 16 Degrees

What is Cos 16 Degrees?

Cos 16 degrees is the value of cosine trigonometric function for an angle equal to 16 degrees. The value of cos 16° is 0.9613 (approx)

How to Find the Value of Cos 16 Degrees?

The value of cos 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 cos 16° is equal to the x-coordinate (0.9613). ∴ cos 16° = 0.9613.

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

Using trigonometric identities, we can write cos 16° in terms of sin 16° as, cos(16°) = √(1 - sin²(16°)). Here, the value of sin 16° is equal to 0.2756.

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

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

• ± √(1-sin²(16°))
• ± 1/√(1 + tan²(16°))
• ± cot 16°/√(1 + cot²(16°))
• ± √(cosec²(16°) - 1)/cosec 16°
• 1/sec 16°

☛ Also check: trigonometric table

What is the Value of Cos 16° in Terms of Cosec 16°?

Since the cosine function can be represented using the cosecant function, we can write cos 16° as [√(cosec²(16°) - 1)/cosec 16°]. The value of cosec 16° is equal to 3.62795.