Cos 6 Degrees

The value of cos 6 degrees is 0.9945218. . .. Cos 6 degrees in radians is written as cos (6° × π/180°), i.e., cos (π/30) or cos (0.104719. . .). In this article, we will discuss the methods to find the value of cos 6 degrees with examples.

• Cos 6°: 0.9945218. . .
• Cos (-6 degrees): 0.9945218. . .
• Cos 6° in radians: cos (π/30) or cos (0.1047197 . . .)

What is the Value of Cos 6 Degrees?

The value of cos 6 degrees in decimal is 0.994521895. . .. Cos 6 degrees can also be expressed using the equivalent of the given angle (6 degrees) in radians (0.10471 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 6 degrees = 6° × (π/180°) rad = π/30 or 0.1047 . . .
∴ cos 6° = cos(0.1047) = 0.9945218. . .

Explanation:

For cos 6 degrees, the angle 6° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 6° value = 0.9945218. . .
Since the cosine function is a periodic function, we can represent cos 6° as, cos 6 degrees = cos(6° + n × 360°), n ∈ Z.
⇒ cos 6° = cos 366° = cos 726°, and so on.
Note: Since, cosine is an even function, the value of cos(-6°) = cos(6°).

Methods to Find Value of Cos 6 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 6° is given as 0.99452. . .. We can find the value of cos 6 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 6 Degrees Using Unit Circle

To find the value of cos 6 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 6° angle with the positive x-axis.
• The cos of 6 degrees equals the x-coordinate(0.9945) of the point of intersection (0.9945, 0.1045) of unit circle and r.

Hence the value of cos 6° = x = 0.9945 (approx)

Cos 6° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 6 degrees as:

• ± √(1-sin²(6°))
• ± 1/√(1 + tan²(6°))
• ± cot 6°/√(1 + cot²(6°))
• ±√(cosec²(6°) - 1)/cosec 6°
• 1/sec 6°

Note: Since 6° lies in the 1st Quadrant, the final value of cos 6° will be positive.

We can use trigonometric identities to represent cos 6° as,

• -cos(180° - 6°) = -cos 174°
• -cos(180° + 6°) = -cos 186°
• sin(90° + 6°) = sin 96°
• sin(90° - 6°) = sin 84°

☛ Also Check:

• cos 90 degrees
• cos 45 degrees
• cos 21 degrees
• cos 690 degrees
• cos 76 degrees
• cos 170 degrees

FAQs on Cos 6 Degrees

What is Cos 6 Degrees?

Cos 6 degrees is the value of cosine trigonometric function for an angle equal to 6 degrees. The value of cos 6° is 0.9945 (approx)

How to Find the Value of Cos 6 Degrees?

The value of cos 6 degrees can be calculated by constructing an angle of 6° with the x-axis, and then finding the coordinates of the corresponding point (0.9945, 0.1045) on the unit circle. The value of cos 6° is equal to the x-coordinate (0.9945). ∴ cos 6° = 0.9945.

How to Find Cos 6° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 6° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(6°))
• ± 1/√(1 + tan²(6°))
• ± cot 6°/√(1 + cot²(6°))
• ± √(cosec²(6°) - 1)/cosec 6°
• 1/sec 6°

☛ Also check: trigonometric table

What is the Value of Cos 6 Degrees in Terms of Tan 6°?

We know, using trig identities, we can write cos 6° as 1/√(1 + tan²(6°)). Here, the value of tan 6° is equal to 0.105104.

What is the Value of Cos 6° in Terms of Sec 6°?

Since the secant function is the reciprocal of the cosine function, we can write cos 6° as 1/sec(6°). The value of sec 6° is equal to 1.005508.